Seminars
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Historic
On least-energy solutions to a pure Neumann Lane-Emden system
2024-10-25
Speaker: Delia Schiera (IST, Lisboa)
I will present some existence results for a Lane-Emden system on a bounded regular domain with Neumann boundary conditions and critical nonlinearities. We show that, under suitable conditions on the exponents in the nonlinearities, least-energy (sign-changing) solutions exist. In the proof...
Trace inequalities for potential operators
2024-09-20
Speaker: Lubos Pick (Charles University, Prague, Czech Republic)
We offer a lateral approach to trace inequalities for potential-type operators based on an appropriate modification of Calderón interpolation theorem. We develop a general theoretical tool for establishing boundedness of notoriously difficult operators (such as potentials) on certain...
Orthogonal Gaussian polyanalytic functions and white noise spectrograms
2024-09-20
Speaker: Luís Daniel Abreu (NuHAG, University of Vienna, Austria)
See attached PDF....
Disproving the Deift conjecture: the loss of almost periodicity
2024-07-05
Speaker: Andreia Chapouto (University of Edinburgh, UK)
The Korteweg-de Vries equation (KdV), derived in the late 1800's to describe shallow-water waves, is one of the simplest but most fundamental examples of a partial differential equation combining nonlinear and dispersive effects. In constructing solutions, we often assume that particular...
On the structure of the infinitesimal generators of semigroups with discrete Lyapunov functionals
2024-04-17
Speaker: Carlos Rocha (Instituto Superior Técnico, Lisbon)
Dynamical systems generated by scalar reaction-diffusion equations enjoy special properties that lead to a very simple structure for the semiflow. Among these properties, the monotone behavior of the number of zeros of the solutions plays an essential role. This discrete Lyapunov functional...
Exploring variations of Carleson's Problem
2024-02-23
Speaker: Shobu Shiraki (Instituto Superior Técnico, Lisboa)
Carleson's problem in harmonic analysis investigates the minimal smoothness required in initial data to ensure almost everywhere convergence in Schrödinger equation solutions. Here, we study two recent variants of the problem: convergence along a curve and convergence for infinitely many...
Viscosity Comparison Theorem for second order spider HJB equations having a "local-time" Kirchhoff's boundary transmission
2024-02-09
Speaker: Isaac Ohavi (Hebrew Univ. of Jerusalem, Israel)
We start this talk by recalling briefly the last results I have obtained on Walsh spider diffusion having a spinning measure selected from the own local time spent by the process at the vertex. We emphasize the key "non-stickiness" property of the process at the junction point, which...
Pontryagin's Maximum Principle for optimization in random environments
2024-02-02
Speaker: Joshué Helí Ricalde-Guerrero (CIMAT, Guanajuato, Mexico)
One of the primary methods for solving optimization problems involves determining a set of necessary conditions for any optimal solution. These conditions can become sufficient under additional convexity assumptions on the objective/constraint functions. Pontryagin's Maximum Principle (PMP)...
Hydrodynamic limit of the multi-component slow boundary WASEP with collisions
2024-01-10
Speaker: Oslenne Nogueira Araújo (CMUC)
In this joint work with Patrícia Gonçalves (IST-ULisboa) and Alexandre Simas (KAUST), we study the hydrodynamic limit for a stochastic interacting particle system whose dynamics consists of a superposition of several dynamics: the exclusion rule, that dictates that no more than a...
Existence and interior regularity of solutions of a fully nonlinear transmission problem
2023-12-15
Speaker: David Stolnicki (Technion - Israel Institute of Technology, Haifa)
Our study delves into the existence and regularity of transmission problems represented by the equation \( \sigma_i(Du) F(D^2u)=f \), concerning regions where \(u>0\) and \(u<0\). This work solves the question on existence of solutions for the problem by utilizing a...
On the embedding between variable Lebesgue space \(L^{p(\cdot)}(\Omega)\) and \(L(LogL)^{\alpha}(\Omega)\) space
2023-11-24
Speaker: Amiran Gogatishvili (Czech Academy of Sciences, Prague, Czech Republic)
We give some sufficient conditions on distribution \( |\{x\in \Omega :\,p(x)\leq 1+\lambda\}|\,(\lambda>0) \) of the exponent function \( p(\cdot): \Omega \to [0,\infty) \) that implies the embedding \( L^{p(\cdot)}(\Omega)\subset L(LogL)^{\alpha}(\Omega)\,(\alpha>0) \),...
Coagulation equations with source leading to anomalous self-similarity
2023-11-17
Speaker: Eugenia Franco (Univ. of Bonn, Germany)
Smoluchowski's coagulation equation describes the evolution in time of a system of atmospheric particles, coagulating upon binary collision. In this talk I will present a generalization of the classical Smoluchowski's coagulation equation, i.e. the coagulation equation with a source term of...
Cumulant hierarchy and chaos in the Kac model
2023-11-02
Speaker: Aleksis Vuoksenmaa (Univ. of Helsinki, Finland)
Kac's (stochastic) model describes the time-evolution of the velocities of homogeneously situated particles that, upon random binary collision, redistribute their kinetic energies in a way that conserves the total energy of the many particle system. In this joint work with Jani Lukkarinen,...
Coagulation equations from applications: existence and mass conservation
2023-11-02
Speaker: Sakari Pirnes (Univ. of Helsinki, Finland)
The Smoluchowski coagulation equation is considered to be one of the most fundamental equations of the classical description of matter alongside the Boltzmann, Navier-Stokes and Euler equations. In this talk, we consider measure valued solutions to multicomponent coagulation equation and...
Localization in multicomponent coagulation systems
2023-10-27
Speaker: Marina Ferreira (CMUC, University of Coimbra)
We study the properties of multicomponent Smoluchowsky coagulation equations. These equations describe the evolution of the number density function over the high-dimensional particle composition space. We show that, under a self-similar scaling, all solutions localize along a line defined by...
Fully nonlinear equations degenerating as a Muckenhoupt weight
2023-10-27
Speaker: David Jesus (Univ. of Bologna, Italy)
We will discuss the regularity of viscosity solutions for fully nonlinear Hessian equations with coefficients in some Muckenhoupt class. We prove Holder and higher regularity under mild assumptions on the coefficients. We use approximation techniques in the spirit of Caffarelli's seminal...
Boundary weak Harnack estimates and regularity for elliptic PDE in divergence form
2023-07-21
Speaker: Fiorella María Rendón García (CMUC, Univ. Coimbra)
See attached file....
Improved regularity for a Hessian-dependent functional
2023-07-21
Speaker: Vincenzo Bianca (CMUC, Univ. Coimbra)
We prove that minimizers of the \( L^d \)-norm of the Hessian in the unit ball of \( \mathbb{R}^d \) are locally of class \( C^{1,\alpha} \). Our findings extend previous results on Hessian-dependent functionals to the borderline case and resonate with the Holder regularity theory available...
Non occurrence of Lavrentiev Phenomenon for functionals with non standard growth
2023-07-11
Speaker: Filomena De Filippis (Univ. of L'Aquila, Italy)
See attached file....
Boundedness and regularity of the solutions of a kind of nonlinear systems
2023-06-23
Speaker: Lubomira Softova (Univ. of Salerno, Italy)
See attached file....
Regularity for fully nonlinear elliptic equations via the fractional Laplacian
2023-04-21
Speaker: Makson Santos (Instituto Superior Técnico, Lisboa)
In the presence of unbounded source terms, we study high-order fractional Sobolev regularity for fully nonlinear, uniformly elliptic equations. Our techniques are based on touching the solution with C1,α cone-like functions to produce a decay rate of the measure of certain sets,...
A multiphase shape optimization problem with measure constraint
2023-04-21
Speaker: Pêdra Andrade (Instituto Superior Técnico, Lisboa)
We study a class of optimal partition problems with measure constraints. We establish the existence of the optimal partition by using a weak formulation that involves a minimization problem where the variables are functions rather than domains. Then, we also prove that...
Metric Fourier approximation of set-valued functions of bounded variation
2023-03-31
Speaker: Elena E. Berdysheva (Univ. of Cape Town, South Africa)
We study set-valued functions (SVFs) mapping a real interval to compact sets in Rd. Older approaches to the approximation of set-valued functions investigated almost exclusively SVFs with convex images (values). The standard methods suffer from convexification. In this talk I will...
Variational solution to Bernoulli type free transmission problems
2023-02-17
Speaker: Harish Shrivastava (Tata Institute of Fundamental Research, Bangalore, India)
In this seminar, I will discuss the regularity theory and some aspects related to free boundaries of variational solutions to Bernoulli type free transmission problems. We start with discussing challenges which come while proving optimal regularity of minimisers when coefficients are only...
(Quasi)-Painlevé equations and Painlevé equivalence problem
2023-01-20
Speaker: Galina Filipuk (Univ. of Warsaw, Poland)
Painlevé equations are second order nonlinear differential equations solutions of which have no movable critical points (algebraic singularities). They appear in many applications (e.g., in the theory of orthogonal polynomials) but in disguise. How to find a transformation to the...
Examples of explicit solutions to the cubic wave equation
2022-12-16
Speaker: Giuseppe Negro (CAMGSD, IST)
We construct a two-parameter family of solutions to the focusing cubic wave equation in $\mathbb{R}^{1+3}$. Depending on the values of the parameters, these solutions either scatter to linear ones, blow-up in finite time, or exhibit a new type of unstable behaviour that acts as a threshold...
Weighted inequalities restricted on the cone of monotone functions and applications in the real interpolation
2022-11-18
Speaker: Amiran Gogatishvili (Czech Academy of Sciences, Prague, Czech Republic)
We consider Hardy inequalities restricted on the cone of monotone and quasi-concave functions and we will give applications of this in the embedding of Lorentz-type spaces and in the real interpolation. Link to access the seminar via...
Improved regularity estimates at free and fixed boundary points
2022-11-04
Speaker: Damião J. Araújo (Univ. Federal da Paraíba, Brazil)
We will discuss local regularity versus regularity estimates at free and fixed boundary points for solutions of degenerate nonlinear elliptic PDEs. We will be interested in showing how precisely the smoothness of a given solution is affected by degenerate diffusion models and free and fixed...
Translating solutions and non-parametric mean curvature flow with prescribed contact angle in Riemannian products
2022-09-30
Speaker: Ilkka Holopainen (Univ. of Helsinki, Finland)
Abstract is attached....
Nonlinear smoothing by the infinite normal form reduction method
2022-07-22
Speaker: Jorge Drumond Silva (IST, Lisboa)
Many nonlinear dispersive partial differential equations exhibit a phenomenon where the nonlinear part of the evolution, in the Duhamel integral formula, is slightly more regular than the purely linear evolution, for the same initial data. This is usually called nonlinear smoothing and is...
The Gelfand problem for the infinity Laplacian
2022-06-03
Speaker: Fernando Charro (Wayne State University, Detroit, USA)
attached....
Hölder and maximal regularity for Hamilton-Jacobi equations
2022-05-27
Speaker: Marco Cirant (University of Padova, Italy)
I will discuss some results on the regularity of solutions to semilinear elliptic equations of Hamilton-Jacobi type. I will in particular focus on the Hölder regularity of solutions, and the problem of L^p maximal regularity, developing two (different?) approaches based on the Bernstein...
Trajectory optimization in \(L^1\) and applications to some new Mean Field Games
2022-05-20
Speaker: Filippo Santambrogio (Université Lyon 1, France)
I will present some regularity results on a variational problem for curves of probability densities where their velocity is penalized in terms of the \( L^1 \) (or total variation) norm, of the time derivative. This is motivated by a new class of Mean Field Games whose goal is to address...
Nonlocal capillarity theory
2022-05-13
Speaker: Enrico Valdinoci (Univ. of Western Australia, Perth, Australia)
We describe some recent results motivated by a nonlocal theory of capillarity, as related to the formation of droplets due to long-range interaction potentials. We will discuss the notion of contact angle in this setting, considering a nonlocal version of the classical Young's Law, together...
A priori estimate for a fully nonlinear problem depending on the gradient
2022-05-06
Speaker: Disson dos Prazeres (Univ. Federal de Sergipe, Brazil)
We will talk about an a priori estimate for positive solutions of some degenerate fully nonlinear elliptic equations where the nonlinearity on the RHS depends on x, u, and ∇u. As a consequence, we use the a priori estimate to establish an existence result....
On the existence of minimizers for Hardy inequalities
2022-04-29
Speaker: Yehuda Pinchover (Technion, Israel Institute of Technology)
TBA ...
Up to the boundary gradient estimates for solutions to nonlinear free boundary problems with unbounded measurable ingredients
2022-04-22
Speaker: Diego R. Moreira (Universidade Federal do Ceará, Brazil)
In this talk, we discuss recent advances on up to the boundary gradient estimates for viscosity solutions of free boundary problems governed by fully nonlinear and quasilinear equations with unbounded coefficients. We present the new Inhomogeneous Pucci Barriers as new elements for the...
Recent results on planar predator-prey and competitive models with seasonality
2022-03-11
Speaker: Carlota Rebelo Gonçalves (Univ. de Lisboa)
TBA...
Minimizing movements for mean curvature flow of partitions
2022-03-04
Speaker: Shokhrukh Kholmatov (Univ. Vienna, Austria)
In this talk I would like to discuss about a weak solution of mean curvature flow of partitions of space, defined via a minimizing movements approach introduced by Almgren-Taylor-Wang and De Giorgi. The talk is based on the joint work with Giovanni Bellettini and Antonin Chambolle....
Pointwise multiplications in Morrey spaces
2022-02-25
Speaker: Yoshihiro Sawano (Chuo Univ., Japan)
The goal of this talk is to discuss the pointwise multiplication
properties of Morrey spaces. First, as a model case,
we consider the Olsen inequality. Second, we discuss
how to specify the pointwise multiplier spaces.
Our method carries over to weak spaces.
This is a joint work mainly...
Nonlinear versions of the Banach-Schauder open mapping theorem
2022-02-04
Speaker: Sauli Lindberg (Univ. Helsinki, Finland)
I will present nonlinear versions of the Banach-Schauder open mapping theorem. They apply to constant-coefficient PDEs (and initial value problems) that are scaling-invariant and preserved under weak-* convergence. As a first application, I will present a partial result on a long-standing...
Regularity theory: from PDE to interfaces and beyond
2022-01-28
Speaker: Edgard Pimentel (CMUC)
Operators with solution-dependent discontinuities give rise to interfaces or free boundaries. In this context, two fundamental questions appear. First, one is interested in the regularity properties of the solutions across the free boundary. Then the analysis focuses on the interfaces and...
A degenerate fully nonlinear free transmission problem with variable exponents
2021-12-17
Speaker: David Jesus (PhD student, CMUC)
In this talk we will discuss optimal regularity for equations with a degeneracy rate which varies in a discontinuous fashion over the domain. Moreover, this discontinuity depends in an implicit way on the solution itself. We introduce the notion of pointwise sharp regularity which requires...
Functions with small and large spectra as (non)extreme points
2021-12-10
Speaker: Konstantin Dyakonov (ICREA & Universitat de Barcelona, Spain)
Let $\Lambda$ be a subset of $\mathbb Z_+:=\{0,1,2,\dots\}$, and let $H^\infty(\Lambda)$ denote the space of bounded analytic functions $f$ on the unit disk whose coefficients $\widehat f(k)$ vanish for $k\notin\La$. Assuming that either $\Lambda$ or $\mathbb Z_+\setminus\Lambda$ is finite,...
Strain and stress-rate type viscoelastic models in the context of implicit constitutive theory
2021-12-03
Speaker:
Yasemin Sengul (Cardiff University, UK)
In the constitutive equations for the classical viscoelastic models, stress tensor is expressed in terms of the strain tensor and its time derivative. However, the classical elastic and viscoelastic models are incapable of explaining the phenomena when the stress is big and the strain is...
Entropy-Transport distances between measures and metric measure spaces
2021-11-12
Speaker: Nicolò De Ponti (SISSA, Trieste, Italy)
See the attached file ...
Relaxed solutions for incompressible inviscid flows: A variational and gravitational approximation to the initial value problem
2021-11-05
Speaker: Ivan Moyano (University of Nice Sophia Antipolis, France)
Following Arnold's geometric interpretation, the Euler equations of an incompressible fluid moving in a domain D are known to be the optimality equation of the minimizing geodesic problem along the group of orientation and volume preserving diffeomorphisms of D. This problem admits a...
Regularity for \(C^{1,\alpha}\) interface transmission problems
2021-07-01
Speaker: María Soria-Carro (UT Austin, USA)
TBA...
Generalizations of the Fourier transform and their applications
2021-06-11
Speaker: Rita Guerra (CMUC)
In this talk, we consider a new generalization of the Fourier transform, depending on four complex parameters and all the powers of the Fourier transform. This new transform is studied in some Lebesgue spaces. We begin with the characterization of each operator by its characteristic...
Bounded weak solutions to elliptic PDE with data in Orlicz spaces
2021-04-23
Speaker: David Cruz-Uribe (Univ. Alabama, USA)
See the attached file...
Entropy dissipation via Information Gamma calculus
2021-04-09
Speaker: Wuchen Li (Univ. South Carolina, USA)
In this talk, we present the convergence behavior for some non-gradient degenerate stochastic differential equations towards their invariant distributions in this talk. Our method extends the connection between Gamma calculus and Hessian operators in the L^2-Wasserstein space. In detail, we...
Besov-Morrey and Triebel-Lizorkin-Morrey spaces with variable exponents
2021-03-05
Speaker: António Caetano (Univ. Aveiro)
Our aim in this talk is to consider Besov-Morrey and Triebel-Lizorkin-Morrey spaces with variable exponents and present some of their properties, in particular the atomic and molecular representations. This reports on joint work with Alexandre Almeida (Besov-Morrey spaces) and Henning Kempka...
The s-numbers, eigenvalues and generalized trigonometric functions
2020-12-18
Speaker: Jan Lang (Ohio State Univ., USA)
Generalized trigonometric functions, which were first introduced by Lundberg 1879, will be discussed together with their connections with p-Laplacian, approximation theory and s-numbers for Sobolev embedding. ...
Sharp inequalities for the Ornstein-Uhlenbeck operator
2020-12-11
Speaker: Lubos Pick (Charles Univ., Prague, Czechia)
The abstract is attached....
Strong solutions of parabolic equations with \(p(x,t)\)-Laplacian: existence and the global regularity properties
2020-11-27
Speaker: Sergey Shmarev (Univ. Oviedo, Spain)
TBA...
Fully nonlinear dead-core systems
2020-11-06
Speaker: Rafayel Teymurazyan (CMUC)
We study fully nonlinear dead-core systems coupled with strong absorption terms. We discover a chain reaction, exploiting properties of an equation along the system. The lack of both the classical Perron's method and comparison principle for the systems requires new tools for tackling the...
Sharp concentration estimates near criticality for sign-changing solutions of Dirichlet and Neumann problems
2020-02-28
Speaker: Hugo Tavares (IST, Univ. Lisboa)
Consider the slightly subcritical problem $-\Delta u_\varepsilon = |u_\varepsilon|^{\frac{4}{n-2}-\varepsilon}u_\varepsilon$ either on $\mathbb{R}^n$ ($n\geq 3$) or in a ball $B$ satisfying Dirichlet or Neumann boundary conditions. For radial solutions, we provide sharp rates and constants...
Sweeping processes and evolution problems with bounded variation
2020-02-14
Speaker: Manuel Monteiro Marques (Univ. Lisboa)
Evolution problems governed by maximal monotone operators with domains that depend on time are present in many areas.The special case of the sweeping process, where the operators are normal cones to time-dependent convex moving sets, was treated by Jean Jacques Moreau in the seventies,...
On q-polynomials: some old and new results
2020-02-07
Speaker: Renato Álvarez-Nodarse (Univ. Sevilla, Spain)
The first family of q-polynomials appears in the works of Stieltjes and at the end of the XIX century, and have been attracted great interest since then. They are related with a lot of pure mathematical problems but also with applied ones. In this talk I will try to give an idea of the...
A two-phase free boundary problem ruled by the infinity laplacian
2019-11-22
Speaker: Damião Araújo (Universidade Federal da Paraíba, Brazil)
In this talk we discuss regularity aspects for solutions of a non-variational two-phase free boundary problem ruled by the infinity Laplacian. This is a joint work with E. Teixeira - University of Central Florida - USA and J.M Urbano - Universidade de Coimbra - PT....
Thermodynamic formalism of non-uniformy expanding maps
2019-11-13
Speaker: Paulo Varandas (UFBA & Univ. Porto)
Ergodic theory is the branch of dynamical systems which aims to describe the asymptotic behavior of almost all orbits, with respect to invariant measures. However there are situations in which such a description is rather trivial, as the case when the invariant measures are finite...
Novel applications of approximation theory to diverse problems in random matrices
2019-10-25
Speaker: Nicholas Witte (Univ. Massey, New Zealand)
We take three contemporary problems arising from random matrices and show how approximation theory is crucial in solving them. However this is not merely an "off-the-shelf" application of known results from within approximation theory, but require extensions beyond the realm of its...
On entropy functionals associated with Bernstein stochastic processes
2019-10-18
Speaker: Pierre Viullermot (Univ. Lorraine & Univ. Lisboa)
Bernstein processes constitute a generalization of Markov processes, and there are many equivalent ways to define them. In this talk I will show how to generate such processes from a hierarchy of forward-backward systems of decoupled deterministic linear parabolic partial differential...
Padé and Padé-type rational and barycentric approximants
2019-07-18
Speaker: M. Redivo-Zaglia (Univ. degli Studi di Padova, Italy)
We consider a particular case of the general rational Hermite interpolation problem where the value of a function f is interpolated at some points, and where the formal series expansions at the origin of the rational interpolant and of f agree as far as...
Sequence Morrey space and Pitt's type theorem
2019-05-31
Speaker:
Leszek Skrzypczak (Adam Mickiewicz Univ., Poznan, Poland)
Morrey (function) spaces and, in particular, smoothness spaces of Besov-Morrey or Triebel-Lizorkin-Morrey type enjoyed a lot of interest recently. Here we turn our attention to Morrey sequence spaces mu,p =mu,p(Zd), 0<p\leq u<\infty, which have yet been considered almost nowhere. They...
Regularity for elliptic equations under minimal assumptions
2019-05-24
Speaker: Giuseppe Di Fazio (Università di Catania, Italy)
Elliptic PDEs are ubiquitous in Mathematics and Sciences. A very important topic concerning elliptic PDEs is the regularity of solutions. We will review some regularity results for linear and quasilinear uniformly elliptic equations. The main focus will be on the minimal assumptions we need...
Dynamics, symmetry and patterns: a tour of Einstein, Ginzburg and Landau
2019-04-12
Speaker: Phillipo Lappicy (USP, Brazil, and IST, Lisbon)
This talk will present my recent results in certain directions within the realm of partial differential equations. On one hand, parabolic equations generate a semiflow in infinite dimensions, and hence we are interested in the dynamical question: what happens when time is large? We will...
Describing the singular behaviour of parabolic equations on cones in fractional Sobolev spaces
2019-04-05
Speaker: Cornelia Schneider (Univ. Erlangen-Nuremberg, Germany)
This talk focusses on the smoothness of the solutions of parabolic PDEs on Lipschitz domains in the fractional Sobolev scale Hs, s in R. The regularity in these spaces is related with the approximation order that can be achieved by numerical schemes based on uniform grid refinements. The...
Evolutionary quasi-variational and variational inequalities with constraints on the derivatives
2019-03-22
Speaker: Lisa Santos (Univ. Minho)
We study the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial derivatives of the solutions. The quasi-linear operators are of monotone type,...
On some applications of orthogonal polynomials in Mathematical-Physics
2019-03-08
Speaker: Renato Álvarez-Nodarse (Univ. Sevilla, Spain)
The orthogonal polynomials (OP) are very useful tools in solving problems not only in Mathematics but also in Physics and Engineering. Among them, the classical orthogonal polynomials (COP) deserve a special attention. The main reasons are, from my point of view, from one hand the fact that...
On function theory in the Euclidean space
2019-01-25
Speaker: Klaus Gürlebeck (Bauhaus-Universität Weimar, Germany)
We consider a function theory for functions defined in Rn with values in the quaternions or in Clifford algebras. The class of monogenic functions is firstly defined as the set of null solutions of a generalized Cauchy-Riemann system. Basic elements of this function theory (see also...
Variational theory and spectral geometry of quantum graphs
2018-12-14
Speaker: James Kennedy (Univ. Lisboa)
The past decade has seen a pronounced growth of interest in differential operators defined on metric graphs, commonly known as quantum graphs. They offer the technical simplicity of one-dimensional objects, while often displaying complex behaviour akin to higher-dimensional ones, and are...
Generalized weighted Lorentz spaces
2018-11-30
Speaker: Amiran Gogatishvili (Czech Academy of Sciences, Prague, Czech Republic)
We will define a new class of generalized weighted Lorentz spaces and we will present some properties of these spaces....
Riemann-Hilbert problems in the theory of orthogonal polynomials
2018-11-23
Speaker: Amílcar Branquinho (CMUC, Univ. Coimbra)
In this talk we survey different aspects of the theory of orthogonal polynomials.Due to the ubiquity nature of orthogonal polynomials in modern science, their study has been performed from very many different points of view. Indeed, they can be considered from a purely algebraic point of...
Porous medium equations with advection
2018-11-16
Speaker: Nicolau Diehl (CMUC)
In this talk we present two types of results: one about decay estimates and another about global existence. Both results are obtained for bounded weak solutions of the Cauchy problem for Porous Medium Equations with advection through a fundamental energy estimate, an L^p -L^q estimate, and...
The existence theorem of weak solution for the initial-boundary problem for Oskolkov's system of equations
2018-10-26
Speaker: Mikhail Turbin (Voronezh State Univ., Russia)
In the talk, the existence of weak solutions of the initial-boundary value problem describing the motion of weakly concentrated aqueous solutions of polymers (Oskolkov's system) is proved. The proof is based on the approximation-topological approach. On the first step, the operator equation...
Investigation of the dynamics of the anti-Zener model
2018-10-12
Speaker: Vladimir Orlov (Voronezh State Univ., Russia)
We prove the solvability in the weak sense of the initial-boundary value problem for the multidimensional fractional model generated by the one-dimensional anti-Zener model. This model takes into account the prehistory of fluid motion along the particle trajectories. This model well...
Polynomial mappings and sieved ultraspherical polynomials. An application involving an electrostatic model
2018-07-20
Speaker: Márcio N. de Jesus (IP Viseu)
We consider orthogonal polynomials (OP) via polynomial mappings in the framework of the semiclassical class. In particular, we analyze in detail cubic transformations for semiclassical OP of class at most 2, giving new examples of semiclassical OP of class 2 and providing integral...
Besov regularity of parabolic PDEs
2018-07-13
Speaker: Cornelia Schneider (Univ. Erlangen-Nuremberg, Germany)
The talk is concerned with the regularity of solutions to linear and nonlinear evolution equations on nonsmooth domains. In particular, we study the smoothness in a specific scale of Besov spaces. The regularity in these spaces determines the approximation order that...
Numerical modelling of cell-renewal, pit patterns and crypt fission in colonic crypts
2018-07-10
Speaker: Giuseppe Romanazzi (UNICAMP, Brazil)
The colonic epithelium is filled in its internal walls by small cavities called crypts. These crypts are small tubular glands, containing proliferative cells, that obey to a programmed cell mechanism. The aberrant crypts occur as a consequence of an abnormal behavior of this programmed...
Aspects of the Painlevé equations
2018-06-22
Speaker: Galina Filipuk (Univ. of Warsaw, Poland)
In this talk I shall present new nonlinear differential-difference equations related to the second Painlevé equation. I shall also review the basics of Nevanlinna theory (notation, examples and main theorems) and show how it can be applied to the study value distribution and growth...
Spectral properties of variable-coefficient Toeplitz matrices
2018-06-15
Speaker: Helena Mascarenhas (CEAFEL, IST Lisboa)
Finite sections of classical Toeplitz matrices have been heavily studied in the last decades due to its several applications in particular to engineering problems. Variable-coefficient Toeplitz matrices generalize these ones. We will present results on the asymtotic behaviour of the ...
Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle
2018-05-11
Speaker: Kenier Castillo (CMUC)
The purpose of this talk is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix similar to a unitary upper Hessenberg matrix ...
Mathematics and the world around us
2018-04-16
Speaker: Renato Álvarez-Nodarse (IMUS, Univ. Sevilla, Spain)
In 1623 Galileo wrote a beautiful book entitled “Il Saggiatore" in which appeared his famous statement that mathematics is the language of science. He claimed that to understand the Universe it is necessary to understand the language in which it is written, and it is written in...
Entropy numbers of compact embeddings or radial and multi-radial subspaces of Sobolev spaces with applications.
2018-04-11
Speaker: Leszek Skrzypczak (Adam Mickiewicz Univ., Poznan, Poland)
See the attached file...
Price models in mean-field games
2018-03-21
Speaker:
Diogo Gomes (KAUST, Saudi Arabia)
In this talk, we introduce a price-formation model for electricity markets where a large number of small players can store and trade electricity. Our model is a constrained mean-field game (MFG) where the price is a Lagrange multiplier for the supply vs. demand balance condition. Under...
Some results on minors of Toeplitz matrices and the theory of symmetric functions
2018-03-16
Speaker: Miguel Tierz (Univ. Lisboa)
We study minors of Toeplitz matrices using the theory of symmetric functions. The symbols of the Toeplitz matrices can either be in the Szegö class or have Fisher-Hartwig singularities and the results apply both to minors of finite and of large dimension. As an application, and also...
A class of electromagnetic p(x,t)-curl systems: existence and uniqueness, blow-up and finite time extinction
2018-02-16
Speaker: Stanislav Antontsev (Univ. Lisboa & Inst. Hydrodynamics, Novosibirsk, Russia)
See the attached file...
On basic Fourier-Bessel expansions. Some related issues.
2018-02-09
Speaker: José Luis Cardoso (CM-UTAD)
We will present a summary of the latest developments with respect to expansions involving the Third Jackson q-Bessel function (or, Hahn-Exton q-Bessel function), with special emphasis regarding Fourier expansions related to some basic functions which are q-analogues...
Global higher regularity of solutions to p(x,t)-parabolic equations
2018-02-09
Speaker: Ivan Kuznetsov (Institute of Hydrodynamics, Novosibirsk, Russia)
See the attached file...
Totalitarian random Tug-of-War games and Jensen's extremal equations
2017-12-15
Speaker: Fernando Charro (CMUC)
See the attached file. ...
Characterization of interpolation between Grand, small or classical Lebesgue spaces
2017-11-24
Speaker: Amiran Gogatishvili (Czech Academy of Sciences, Prague, Czech Republic)
See the attached file....
Regularity of interfaces for a Pucci type segregation problem
2017-11-17
Speaker: Verónica Quítalo (CMUC, Univ. Coimbra)
In this talk we will start giving a brief review about a segregation model with nonlinear diffusion that evolve to a free boundary problem as a motivation for our problem. Then we will present our latest results for the regularity of the limit solution as well as the regularity of the free...
The faceless problem
2017-11-03
Speaker: F. J. García-Pacheco (Univ. Cadiz, Spain)
Internal points were introduced in the literature of topological vector spaces to characterize the nest locally convex vector topology. Later on, they have been generalized to the context of real vector spaces by means of the inner points. Inner points can be seen as the most opposite...
First-order, stationary mean-field games with congestion
2017-10-27
Speaker: Levon Nurbekyan (KAUST, Saudi Arabia)
Mean-field games (MFGs) are models for large populations of competing, rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. In this talk, I will present a recent contribution...
Embeddings of weighted Morrey spaces
2017-09-29
Speaker: Dorothee Haroske (Univ. Jena, Germany)
See the attached file...
Lagrangian controllability for the 3D Navier-Stokes equations
2017-09-27
Speaker: Vahagn Nersesyan (Univ. Versailles, France)
In the Eulerian approach, the motion of an incompressible fluid is usually described by the velocity field which is given by the Navier-Stokes system. The velocity field generates a flow in the space of volume-preserving diffeomorphisms. The latter plays a central role in the Lagrangian...
Overlapping domain decomposition algorithms for singularly perturbed parabolic problems
2017-06-28
Speaker: Sunil Kumar (Indian Institute of Technology, India)
in the attached file...
On a quadratic Schrödinger system
2017-06-16
Speaker: Filipe Oliveira (Univ. Nova de Lisboa)
See the attached file...
Radial and block-radial subspaces of Sobolev and Besov spaces: regularity, decay and compactness
2017-06-09
Speaker: Leszek Skrzypczak (Adam Mickiewicz Univ., Poznan, Poland)
See the attached file...
Analytical and numerical methods for a class of second and third kind Volterra integral equations
2017-06-02
Speaker: Sonia Seyed Allaei (CMUC)
See the attached file. ...
On Besov spaces of smoothness zero
2017-05-26
Speaker: Oscar Domínguez (CMUC)
see the attached file...
On a generalized nonlinear heat equation in Besov and Triebel-Lizorkin spaces
2017-05-10
Speaker: Franka Baaske (Friedrich-Schiller-Univ. Jena, Germany)
See the attached file...
The \(\theta\)-parareal schemes
2017-05-03
Speaker: Richard Tsai (Univ. of Texas at Austin, USA)
We propose a variant of the parareal method for parallel-in-time computation of time dependent problems. We call it the θ-parareal schemes because it formally resembles the θ-schemes for discretizing time dependent partial differential equations. We analyze the linear stability of...
Morrey spaces on domains: different approaches and growth envelopes
2017-04-28
Speaker: Cornelia Schneider (Univ. Erlangen-Nuremberg, Germany)
see the attached file...
A symbolic approach to perturbed second degree forms: study of the case of perturbed Chebyshev polynomials
2017-04-19
Speaker: Zélia Rocha (CMUP, Univ. Porto)
See the attached file....
Fast algorithms for high frequency wave propagation
2017-04-12
Speaker: Bjorn Engquist (Univ. of Texas at Austin, USA)
Direct numerical approximation of high frequency wave propagation typically requires a very large number of unknowns and is computationally very costly. We will discuss two aspects of this type of problem. One is the development and analysis of fast algorithms...
General monotonicity concept and its applications
2017-04-07
Speaker: Sergey Tikhonov (CRM, Barcelona, Spain)
TBA...
Characterization of Sobolev spaces through functionals without derivatives dependence
2017-03-17
Speaker: Ana Margarida Ribeiro (CMA, Univ. Nova de Lisboa)
Extending previous works due to Bourgain, Brézis, and Mironescu [J. Anal. Math. 87 (2002)] and Leoni and Spector [J. Funct. Anal. 261, 10 (2011)], we provide new characterizations of Sobolev spaces in terms of functionals involving difference quotients. These characterizations have...
Paths to uniqueness of critical points and applications
2017-02-17
Speaker: Hugo Tavares (U. Lisboa)
In this talk we show a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our method relies on convexity properties along suitable paths. To illustrate our method we present a...
Approximation in Morrey spaces
2017-02-03
Speaker: Alexandre Almeida (Univ. Aveiro)
We introduce a new subspace of Morrey spaces where the approximation by nice functions is possible in Morrey norm. In particular, we obtain an explicit description of the closure of the set of all infinitely differentiable compactly supported functions in Morrey spaces....
Multiple orthogonal polynomials and some of their applications
2017-01-26
Speaker: Walter Van Assche (KU Leuven, Belgium)
Multiple orthogonal polynomials are polynomials in one variable that satisfy orthogonality conditions with respect to several measures. I will briefly give some general properties of these polynomials (recurrence relation, zeros etc.). These polynomials have recently appeared in many...
Systems of partial differential equations arising from population dynamics and neuroscience: Free boundary problems as a result of segregation
2016-12-14
Speaker: Verónica Quítalo (Univ. Coimbra - CoLab UT Austin Portugal Program)
In this talk we will present some two phase free boundary problems arising from population dynamics. We will focus on systems with fully nonlinear diffusion and local interaction, and linear systems with a (non local) long range interaction. In the long range model, the growth of a...
Geometric regularity theory for fully nonlinear elliptic equations
2016-12-07
Speaker: Edgard A. Pimentel (Univ. São Carlos, Brazil)
In this talk, we examine the regularity theory for fully nonlinear elliptic equations of the form F(D^2 u)=f(x) where F is a (λ,Λ)-elliptic operator and f:B1→ℝ is a continuous source term, in appropriate Lebesgue spaces. We recur to a set of tools known as geometric-...
The C^{p'}-regularity conjecture in the plane
2016-11-25
Speaker: Damião Araújo (UNILAB and UFPB, Brazil)
We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are...
The embeddings of Jawerth and Franke for Besov and Triebel-Lizorkin spaces with variable exponents
2016-11-04
Speaker: Helena Gonçalves (Technische Univ. Chemnitz, Germany)
See the attached file...
Group theory and special functions theory: a two way street
2016-10-19
Speaker: R. Álvarez-Nodarse (Univ. Sevilla, Spain)
It is well known the role of symmetries in Science and, particular, in the Physical Sciences. Almost all physical laws are consequence of symmetries. Take as an example the conservation laws of Classical Mechanics and the Noether's theorem. Another interesting example is related to...
Reconstruction of complex-valued once differentiable conductivities in 2D
2016-10-14
Speaker: Evgeny Lakshtanov (Univ. Aveiro)
The classical dbar-method has been generalized recently by Lakshtanov, Novikov, Vainberg to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem without assumptions on smoothness of potentials. As a consequence, this provides...
The extension operator in variable exponent function spaces
2016-10-12
Speaker: Henning Kempka (Technische Univ. Chemnitz, Germany)
The abstract is in the attached pdf file...
The variable coefficients thin obstacle problem
2016-09-23
Speaker: Wenhui Shi (CMUC)
See the attached file....
On a fractional Monge-Ampère operator
2016-09-16
Speaker: Fernando Charro (UPC, Barcelona, Spain)
See the attached file. ...
On Laguerre-Hahn orthogonal polynomials of class one
2016-06-17
Speaker: Maria das Neves Rebocho (Univ. Beira Interior & CMUC)
We study recurrences for Laguerre–Hahn orthogonal polynomials of class one. It is shown for some families of such Laguerre–Hahn polynomials that the coefficients of the three term recurrence relation satisfy some forms of discrete Painlevé equations, namely dPI and...
On the works of A. Markov and Stieltjes on monotonicity of zeros
2016-05-27
Speaker: Kenier Castillo (CMUC)
We discuss, in this didactical talk, old and new results on the monotonicity of zeros of polynomials paying special attention to the flexibility and versatility of the works of A. Markov and Stieltjes on the subject....
Sobolev spaces with power weights perturbed by slowly varying functions
2016-05-13
Speaker: Therese Mieth (Friedrich-Schiller-Univ. Jena, Germany)
See the attached file...
A model for phase transitions with competing terms
2016-05-12
Speaker: Margarida Baía (IST, Lisboa)
In this work we study, via $\Gamma$-convergence techniques, the asymptotic behaviour of a family of coupled singular perturbations of a non-convex functional of the type $$\int_\Omega f(u(x),\nabla u(x),\rho(x)) \, dx $$ as a variational model to address two-phase transitions problems...
Gradient estimates for the porous medium equation
2016-04-22
Speaker: Juhana Siljander (Univ. Jyväskylä, Finland)
The sharp regularity of weak solutions to the porous medium equation is a long-standing open problem. The fundamental solution of the problem, the so called Barenblatt solution, is known to be C^{1/(m-1)}-Hölder continuous, and it is a natural question whether this is the worst possible...
Numerical investigations of spatially segregation models
2016-04-13
Speaker: Farid Bozorgnia (IST, Univ. Lisboa)
In this talk, we consider different models of Reaction-Diffusion system which describe the interactions between biological components. Thesemodels are:Adjacent segregation: The adjacent segregation model has been studied extensively [2]. In this model particles annihilate on contact, and...
Banach Frames and Banach Gelfand Triples, with applications to Time-Frequency Analysis
2016-04-06
Speaker: Hans G. Feichtinger (Univ. Vienna, Austria)
It is the purpose of this talk to discuss essentially two concepts which arose in the context of time-frequency analysis (specifically relevant for Gabor Analysis), but which represent useful and fundamental functional analytic tools which certainly will be very useful also in quite...
Some results in the context of structured deformations
2016-04-01
Speaker: José Matias (IST, Lisboa)
Structured deformations provide a model to non-classical deformations of continua suitable for the description of deformations of materials whose kinematics requires analysis at both the macroscopic and microscopic levels. We present an overview of the theory and discuss different...
On convolution type operator with piecewise continuous symbols on variable Lebesgue spaces
2016-02-26
Speaker: Oleksiy Karlovych (Univ. Nova de Lisboa)
See the attached file. ...
Non-smooth atomic decomposition of 2-microlocal spaces with variable integrability
2016-02-19
Speaker: Helena Gonçalves (Technische Univ. Chemnitz, Germany)
The abstract is in the attached pdf file...
On mixed and stabilized finite element methods for the obstacle problem
2016-02-12
Speaker: Juha Videman (IST, Univ. Lisboa)
The abstract is in the attached pdf file...
Systems of PDEs in porous media
2016-02-05
Speaker: Léonard Monsaingeon (IST, Lisboa)
In this talk I will investigate systems of parabolic PDEs in porous media, describing competitive adsorption phenomena in groundwater contaminant models. The system is degenerate and does not fall into the general class of models studied by Alt and Luckhaus, mainly due to the non-convex...
From medical images to computational hemodynamics: a robust pipeline
2015-12-09
Speaker: Ana J. João (CEMAT-IST, ULisboa)
In the past decade, with the proliferation of technology and the increase of its capability, Computational Fluid Dynamics (CFD) has become a popular tool in several applications. This combined with our desire of increasing human life expectancy has lead to the combination of CFD and...
Relaxation in BV×Lp
2015-11-13
Speaker: Graça Carita (Univ. Évora)
An integral representation result is obtained for the relaxation of a class of energy functionals depending on two vector fields u in BV and v in Lp with 1<p≤+∞. This energy have been introduced to deal with equilibria for systems depending on...
A distance on the space of Radon measures with application to spatial population dynamics
2015-10-23
Speaker: Stanislav Kondratyev (CMUC, Univ. Coimbra)
We introduce a new optimal transport distance between nonnegative finite Radon measures, derive associated Riemannian structure and develop an Otto calculus. As an application, we identify a model in spatial population dynamics as a gradient flow and obtain long-time convergence...
Approximation numbers of weighted Sobolev embeddings via bracketing
2015-10-02
Speaker: Therese Mieth (Friedrich-Schiller-Univ. Jena, Germany)
...
On the discriminated nondimensionalization of coupled, non-linear ordinary differential equations and system of equations
2015-07-24
Speaker: Manuel Conesa (Univ. Politécnica de Cartagena, Spain)
The first step to simplify the analysis of a mathematical model is to search the dimensionless groups that control its solution pattern since the solution of any equation or system of equations that define the laws that rule a physical or engineering problem can be represented as a relation...
Object detection, multispectral fusion, motion analysis and tracking in aerial imagery and video
2015-07-08
Speaker: Kannappan Palaniappan (Univ. Missouri, Columbia, USA)
Visual feature-based tracking systems need to adapt to variations in the appearance of an object and in the scene for robust performance to avoid drift. Tracking in aerial imagery is challenging as viewing geometry, calibration inaccuracies, complex flight paths and back- ground changes...
Filtering, fusion, detection and segmentation of microvasculature vessel fluorescence imagery
2015-07-07
Speaker: Kannappan Palaniappan (Univ. Missouri, Columbia, USA)
Automatic segmentation of three-dimensional microvascular structures is needed for quantifying morphological changes and remodeling of blood vessels during development, disease and treatment processes. We use an approach for vessel segmentation that combines multiple single focus images use...
Regularity properties of maximal functions
2015-06-08
Speaker: Emanuel Carneiro (IMPA, Rio de Janeiro, Brazil)
In this talk I will briefly survey the regularity theory for maximal operators in Sobolev and BV spaces. It has been conjectured for more than a decade that the classical centered one-dimensional Hardy-Littlewood maximal operator should not increase the variation of a function. The...
Invariant manifolds of non-autonomous ODEs
2015-05-29
Speaker: António Bento (Univ. Beira Interior)
...
Boundedness of Stein's spherical maximal function in variable Lebesgue space and application to the wave equation
2015-05-15
Speaker:
Amiran Gogatishvili (Czech Academy of Sciences, Czech Republic)
The abstract is in the attached pdf file...
Harmonic Analysis for the Natural Sciences II
2015-04-24
Speaker: Luís Daniel Abreu (ARI-Austrian Academy of Sciences)
This is a continuation of Wednesday's talk on the Numerical Analysis seminar. After a short presentation of the program, I will focus on the new approach to the localization problem which is being developed with João M. Pereira, a former student of DMUC....
Kinetic theory of simple reacting spheres: modelling and hydrodynamic regimes
2015-04-17
Speaker: Ana Jacinta Soares (Univ. Minho)
In the frame of the kinetic theory of chemically reacting gases, we consider the model of simple reacting spheres (SRS) in a moderately dense gas regime. The gas molecules behave as if they were single mass points and collisions result in chemically reactive encounters when the kinetic...
An optimal design problem with fractional diffusion
2015-04-10
Speaker: Rafayel Teymurazyan (CMUC)
We study an optimization problem ruled by a-fractional diffusion operator with volume constraint. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of class C0,\alpha, and that the free boundary is a C1,\alpha surface, up to a...
About embeddings and minimal action solutions of elliptic equations
2015-03-13
Speaker: Eugénio Rocha (Univ. Aveiro)
in the attached file ...
Orthogonal polynomial interpretation of \Delta-Toda and Volterra lattices
2015-02-27
Speaker: Ana Foulquié Moreno (Univ. Aveiro)
The correspondence between dynamics of $\Delta$-Toda and $\Delta$-Volterra lattices for the coefficients of the Jacobi operator and its resolvent function is established. A method to solve inverse problem --integration of $\Delta$--Toda and $\Delta$-Volterra lattices -- based on Pad\'e...
A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations
2015-02-06
Speaker: Léonard Monsaingeon (IST, Univ. Lisboa)
The abstract is in the attached pdf file...
Compactness in quasi-Banach function spaces
2015-01-23
Speaker: António Caetano (Univ. Aveiro)
The well-known criterion for the precompactness of sets in a Banach function space states that a subset K of the absolutely continuous part Xa of a Banach function space X is precompact in X if and only if K is locally precompact in measure and K has uniformly absolutely...
Orthogonal polynomials and random matrices
2014-11-28
Speaker: Alfredo Deaño (Univ. Carlos III, Madrid, Spain)
In this talk we present some classical results on unitarily invariant ensembles of random matrices of size NxN, the prime example being the Gaussian Unitary Ensemble (GUE). It will be shown how the analysis of the corresponding family of orthogonal polynomials on the real line can be used...
Bi-periodic solutions to the Fokker-Planck equation and operation of Brownian motors
2014-11-21
Speaker: Dmitry Vorotnikov (CMUC, Univ. Coimbra)
We study the unidirectional transport effect for Brownian ratchets modeled by Fokker--Planck-type equations. In particular, we consider the adiabatic andsemiadiabatic limits for tilting ratchets, generic ratchets with small diffusion, and the multi-state chemical ratchets. Having...
Uniform convergence of Hermite-Padé approximants for systems of Markov type functions
2014-10-24
Speaker: Sergio Medina Peralta (Univ. Carlos III, Madrid, Spain)
This talk deals with simultaneous rational approximation. In particular we study Hermite-Padé approximants of analytic and meromorphic functions of Markov type. The central results of this work is about of convergence of type I Hermite-Padé approximants of a Nikishin system....
Limiting embeddings in smoothness Morrey spaces, and applications
2014-10-03
Speaker: Dorothee D. Haroske (Univ. Jena, Germany)
...
Electrostatic interpretation of roots of polynomials satisfying certain 2nd order differential equations
2014-09-19
Speaker: Edmundo Huertas Cejudo (CMUC)
In the last years some attention has been paid to the so called canonical spectral transformations of measures. This talk is focused on the behaviour of zeros of monic orthogonal polynomial sequences (MOPS in short) associated with the so called Geronimus canonical transformation, which...
Mehler-Heine asymptotics of polynomials
2014-07-16
Speaker: Juan J. Moreno Balcázar (Univ. Almeria, Spain)
In this talk, we will give an overview about Mehler--Heine asymptotics of polynomials. This type of formulae is well known for very classical Jacobi, Laguerre and Hermite polynomials. We pay attention to recent results obtained for other families of polynomials such as generalized...
The spectral theorem on the para-orthogonality theory
2014-07-16
Speaker: Kenier Castillo (UNESP, Brazil)
Our goal is to provide the para-orthogonality theory with a new powerful tool for computing: recurrence relation. Analogous results to the classicals Favard and Geronimus-Wendroff theorems are deduced....
Compact embeddings of weighted Sobolev spaces
2014-07-11
Speaker: Therese Mieth (Friedrich-Schiller-Univ. Jena, Germany)
The abstract is in the attached pdf file ...
Generalizations of generating functions for orthogonal polynomials in the Askey and q-Askey schemes
2014-07-09
Speaker: Howard S. Cohl (National Institute of Standards and Technology, USA)
In this talk, we present generalized generating functions for generalized hypergeometric and basic hypergeometric orthogonal polynomials. These generalized expansions are obtained by re-expressing the polynomials in the generating functions using multi-parameter connection relations. The...
Boundary integral methods using implicitly defined interfaces and their applications
2014-06-20
Speaker: Richard Tsai (Univ. of Texas at Austin, USA)
I will describe a new framework for building numerical methods for boundary integral equations using implicit surface representation. Such setting is natural for many problems that involve bulk-diffusion driven nonlinear interface dynamics in irregular and unbounded domains. Typically the...
Medical image processing using the image derivatives
2014-05-23
Speaker: Alberto Gambaruto (Barcelona Supercomputer Center, Spain)
Medical image processing remains an active field of research principally due to the difficulty of defining the problem. The most successful approaches are related to solving PDEs that model anisotropic diffusion, where the anisotropy is given spatially by the image gradient or Laplacian,...
Pattern formation on evolving biological surfaces: the surface fi nite element method applied to reaction-diff usion systems
2014-05-16
Speaker: Raquel Barreira (IP Setúbal)
The abstract is in the attached pdf file...
A parabolic Harnack inequality for a nonlocal in time diffusion equation
2014-04-09
Speaker: Juhana Siljander (Univ. Helsinki, Finland)
Nonlocal PDEs have gathered a lot of interest during the last years. In particular, the fractional Laplacian and its generalizations have been studied extensively recently. In this talk we will discuss a different kind of nonlocal equation: namely a parabolic diffusion model where the ...
Weighted Sobolev orthogonal polynomials on the unit ball
2014-04-09
Speaker: Miguel Piñar (Univ. Granada, Spain)
For the classical weight function on the unit ball, a Sobolev inner product involving the gradient operator is considered. For this inner product a family of mutually orthogonal polynomials on the unit ball is constructed in terms of spherical harmonics and a sequence of Sobolev orthogonal...
Generalized Bargmann transforms attached to Landau levels
2014-04-04
Speaker: Zouhair Mouayn (Univ. Coimbra)
We construct a family of generalized Bargmann transforms mapping isometrically the states Hilbert spaces of specific Hamiltonian operators onto L2-eigenspaces associated with Landau levels of a uniform magnetic field on the Euclidean plane, the Poincaré disk and the Riemann...
Educational interfaces between Mathematics and Industry. Report on an ICMI-ICIAM Study.
2014-04-04
Speaker: Rudolf Strässer (J.L. Univ. Giessen, Germany & A.C. Univ. Brisbane, Australia)
The presentation will offer some results of the joint ICMI-ICIAM-study on "Educational Interfaces between Mathematics and Industry (EIMI)", which finished in 2013. Elaborating on Mathematics in these different institutions, it will briefly present the role of...
Universality laws for time-frequency ensembles
2014-03-28
Speaker: Luís Daniel Abreu (ARI-Austrian Acad. of Sciences)
There is a transdisciplinar idea known as "Universality" which aims to understand how the macroscopic laws of nature can be obtained from those ruling the microscopic world. The following phenomenon seems to be pervasive: often, a system of interacting objects (for instance,...
On special class of para-orthogonal polynomials
2014-03-21
Speaker: Kenier Castillo (Univ. Estadual Paulista, Sao Paulo, Brazil)
We study the zeros in connection with perturbed recurrence coefficients of polynomials satisfying a certain three-term recurrence relation. As a particular case, we consider the Askey para-orthogonal polynomials on the unit circle, ${_2}F_1(-n, a+b i; 2 a; 1-z)$, $a,b \in \re$,...
Wasserstein metric and seismic exploration
2014-03-12
Speaker: Bjorn Engquist (Univ. of Texas at Austin, USA)
In seismic exploration a wave field is generated at the surface and reflections from the earths interior are recorded. The purpose is to find properties such as wave velocity and location of reflecting sub layers. This can be in an inverse problem where the ...
Non local phase transitions
2014-03-07
Speaker: Yannick Sire (Univ. d'Aix-Marseille, France)
I will describe a few recent results dealing with the Allen-Cahn equations with a fractional laplacian. The results are in connection with a fractional version of a conjecture by De Giorgi. I will also explain several open problems and what is the state of the art....
Orthogonal polynomials associated with Laguerre weight matrix
2014-03-05
Speaker: Nikta Shayanfar (K. N. Toosi Univ. of Technology, Tehran, Iran)
We study a sequence of matrix polynomials (Pn)n of size nxn, which are orthogonal with respect to the weight matrix involving the classical Laguerre scalar weight. This family of orthogonal matrix polynomials satisfy a second order differential equation with coefficients ...
Bullwhips, conservation laws and 1-Laplacian
2014-02-07
Speaker: Dmitry Vorotnikov (CMUC, Univ. Coimbra)
We study the equation of motion for inextensible strings with the "whip" boundary conditions. We prove existence of generalized Young measure solutions after transforming the equation into a system of conservation laws and approximating it with a regularized system...
A Cohen type inequality for Laguerre-Sobolev expansions
2014-01-31
Speaker: Maria Francisca Perez Valero (Univ. Carlos III, Madrid, Spain)
In the framework of approximation theory, a Cohen type inequality is a lower bound for the norm of the partial sums of the Fourier expansions in terms of a certain orthogonal system. This kind of inequalities have been investigated by many authors in various contexts and forms, including...
Attractors of trajectory spaces in fluid mechanics
2014-01-10
Speaker: Stanislav Kondratyev (CMUC, Univ. Coimbra)
It often happens in fluid mechanics that initial and boundary value problems are not known to be uniquely solvable. In this case the dynamics can be appropriately treated in terms of trajectory spaces. The talk will review a few concepts of attractors applicable to trajectory...
The symmetrization problem in the theory of multiple orthogonal polynomials
2013-12-06
Speaker: Edmundo Huertas Cejudo (CMUC, Univ. Coimbra)
For a symmetric sequence of type II multiple ortogonal polynomials satisfying a high-term recurrence relation, we provide the relationship between the Weyl function associated to the corresponding block Jacobi matrix and the Stieltjes matrix function. Next, from an arbitrary (and not...
Dynamics and interpretation of some integrable systems via orthogonal polynomials
2013-11-22
Speaker: Amílcar Branquinho (CMUC, Univ. Coimbra)
We establish the correspondence between a non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair. We study the solution of the discrete dynamical system, giving explicit expressions for the resolvent function associated with...
Essential spectrum for graphs of radial functions
2013-11-08
Speaker: Fábio Montenegro (UFC, Brazil)
We prove that if M is a complete hypersurface in R^{n+1} which is the graph of a real radial function, then the spectrum of the Laplace operator on M is the interval [0, \infty)....
On the weak-approximate fixed point property
2013-11-08
Speaker: Cleon Barroso (UFC, Brazil)
In this talk we will present a research line known as weak-approximate fixed point property. Some related problems and contributions will be addressed. We will also present some interesting applications related to the fixed point theory, and also to the theory of ordinary differential...
Boundedness for some doubly nonlinear parabolic PDEs
2013-10-25
Speaker: Eurica Henriques (CM/UTAD)
We show that, in the setting of measure spaces equipped with a doubling non-trivial Borel measure $\mu$, of dimension $d_\mu$, supporting a weak Poincaré inequality, the nonnegative weak subsolutions of the doubly nonlinear equation $(u^{q})t-\div{(|\nabla u|^{p-2}\nabla u)}=0, ...
Obstacle problems in variable exponent Sobolev spaces
2013-10-18
Speaker: Rafayel Teymurazyan (CMAF, Univ. Lisboa)
We are going to discuss the obstacle problem for a quite large class of heterogeneous quasi-linear degenerate elliptic operators in variable exponent Sobolev spaces (Orlicz-Sobolev spaces). We see that the solution has C^{1,\alpha}_{loc} regularity for some \alpha\in (0,1) and prove...
A quantitative Hölder exponent for the non-homogeneous p-parabolic equation
2013-10-04
Speaker: José Miguel Urbano (CMUC, Univ. Coimbra)
That weak solutions of degenerate parabolic pdes modelled on the inhomogeneous p-Laplace equation are Hölder continuous is known for almost 30 years. What was hitherto missing from the literature was a precise and sharp knowledge of the Hölder exponent in terms of p, the...
Regularity for anisotropic fully nonlinear integro-differential equations
2013-07-12
Speaker: Raimundo Leitão (Univ. Coimbra)
We consider fully nonlinear integro-differential equations governed by kernels that have different homogeneities in different directions. We derive a nonlocal version of the ABP estimate, a Harnack inequality, and interior regularity. We show the estimates are stable as the smallest degree...
Free boundary problems and geometric regularity theory
2013-06-21
Speaker: Eduardo Teixeira (Univ. Federal do Ceará, Brazil)
I will discuss a new geometric approach to problems related to regularity issues for elliptic and parabolic problems. Motivated by fundamental questions from the theory of free boundary problems, this new set of tools has been shown to be rather efficient in the solution of a number...
A chromaticity-brightness model for imaging processing in a "u + v" framework
2013-06-14
Speaker: Rita Gonçalves Ferreira (IST/CMA)
In imaging processing many important issues arise such as image segmentation, color restoration, and image denoising. A rigorous mathematical analysis is needed to validate the extensive numerical analysis literature in this field, and to open new avenues on image...
Weak solvability of one model of dynamics of thermoviscoelastic continuous medium with regularized objective Jaumann derivative
2013-05-17
Speaker: Victor Zvyagin (Voronezh State Univ., Russia)
In the talk, we establish the weak solvability of the initial–boundary value problem for the model of dynamics of thermoviscoelastic continuous medium which rheological relations (constitutive laws) contains regularized objective Jaumann’s derivative. The investigation is carried...
Riesz and Wolff potentials in variable exponent Lebesgue spaces
2013-05-10
Speaker: Alexandre Almeida (Univ. Aveiro)
We study mapping properties of Riesz and Wolff potentials in Lebesgue spaces with variable exponent. Our approach includes the limiting case corresponding to potentials of L1 functions. This case is particularly interesting in the study of some nonlinear PDEs. ...
(1,1)-Coherent pairs on the unit circle
2013-04-26
Speaker: Natalia Camila Pinzón Cortés (Univ. Carlos III, Madrid, Spain)
see file...
Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line
2013-04-12
Speaker: Maria das Neves Rebocho (Univ. Beira Interior/CMUC)
The main purpose of the talk is to introduce matrix Sylvester differential equations in the study of Laguerre-Hahn orthogonal polynomials.It is shown an equivalence between the scalar Riccati differential equation for the Stieltjes function and matrix Sylvester differential equations for...
Coherent states quantization and formulae for the Berezin transform
2013-04-05
Speaker: Zouhair Mouayn (Univ. Sultan Moulay Slimane, Morocco)
We are concerned with bound states eigenspaces of the Schrodinger operator with magnetic field in Cn and in the complex unit ball Bn. We construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover...
Zero behavior of certain perturbed ortogonal polynomials
2013-02-22
Speaker: Edmundo Huertas Cejudo (Univ. Coimbra)
This talk is focused in the so called canonical spectral transformations of measures. We analyze the behaviour of zeros of MOPS associated with the Christoffel and Uvarov transformations of the measures. First, we introduce the representation of the perturbed MOPS in terms of the initial...
Regularity for some doubly nonlinear evolutionary equations in measure spaces
2013-02-01
Speaker: Rojbin Laleoglu (CM, Univ. Trás-os-Montes e Alto Douro)
We will consider the regularity question for the nonnegative weak solutions of certain doubly nonlinear parabolic equations falling into a very large and important class of equations, namely the class of degenerate and singular equations. These type of evolutionary equations appear in the...
Linear potentials in nonlinear potential theory
2013-01-04
Speaker: Tuomo Kuusi (Aalto Univ., Helsinki, Finland)
We give an update to some aspects of the theory for solutions to nonlinear elliptic or parabolic, possibly degenerate, equations involving p-Laplacean type operators and datum, which, in full generality, can be a measure. The main focus is to describe recent pointwise potential estimates for...
Dirichlet problem in a domain with a small hole
2012-11-23
Speaker: M. Dalla Riva (CIDMA, Univ. Aveiro)
We consider a Dirichlet problem in a domain with a small hole of diameter proportional to a real parameter $\epsilon$ and we denote by $u_\epsilon$ the corresponding solution. We show that the behavior of $u_\epsilon$ for $\epsilon$ small and positive can be described in terms of real...
On difference-differential equations for deformed Laguerre-Hahn orthogonal polynomials on the unit circle
2012-11-09
Speaker: Amílcar Branquinho (CMUC, Univ. Coimbra)
In this talk we study sequences of orthogonal polynomials on the unit circle whose Carathéodory function satisfies a Riccati-type differential equation with polynomial coefficients. We deduce discrete Lax equations which lead to difference equations for the corresponding sequences of...
Variational models for image segmentation
2012-10-26
Speaker: Juan Carlos Moreno (CMUC)
In imaging science, texture and multiphase image segmentation are two problems of great interest. The importance of image segmentation models lies in looking for the best representation of an image into meaningful information by partitioning it into well distinguished regions containing some...
Regularity and geometric estimates for minima of discontinuous and singular functionals
2012-10-12
Speaker: Raimundo Leitão (Univ. Coimbra)
This work consists of two parts: In the first part we study nonnegative minimizers of degenerate elliptic functionals for variational kernels that are discontinuous. The Euler-Lagrange equation is therefore governed by a non-homogeneous, degenerate elliptic equation with free boundary...
An heterogeneous multiscale method for Aberrant Crypt Foci dynamics
2012-09-28
Speaker: Giuseppe Romanazzi (CMUC)
Assuming that Aberrant Crypt Foci (ACF) in the colon are consequence of accumulation of abnormal cells we will characterize the dynamics of these cells, in order to describe the evolution of ACF. The colon will be considered as a periodic spread structure composed by a crypt and...
Local Hölder continuity for doubly nonlinear parabolic equations
2012-06-29
Speaker:
José Miguel Urbano (CMUC/Univ. Coimbra)
We give a proof of the Hölder continuity of weak solutions for the doubly nonlinear parabolic equation in the degenerate case. The analysis discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling...
Interpolation of uniformly absolutely continuous operators
2012-06-22
Speaker: Bohumir Opic (Charles Univ., Prague, Czech Republic)
We develop a method suitable for interpolation of uniformly absolutely continuous operators. We apply this method to establish compactness of operators and embeddings especially in the limiting situations, where the classical interpolation methods fail. We study types of certain ...
Multivariate Sobolev orthogonal polynomials on the ball
2012-06-15
Speaker: Miguel Piñar (Univ. Granada, Spain)
Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding the evaluation of derivatives at several points to a measure, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be...
Receiver Operator Characteristic Curves in the evaluation of medical diagnosis
2012-06-06
Speaker: Pedro Oliveira (Instituto de Ciências Biomédicas Abel Salazar, Univ. Porto)
The origin of Receiver Operating Characteristic (ROC) analysis can be traced to the theory of statistical decision making, related to applications in signal detection and psychology and, over the years, has become a powerful tool for measuring diagnostic tests performance in medicine. A...
Riemann Hilbert problems on a Riemann surface and on the complex plane
2012-05-25
Speaker: Maria Teresa Malheiro (Univ. Minho)
We study the solvability of scalar Riemann-Hilbert problems relative to a contour on a torus which are equivalent to some matrix Riemann-Hilbert problems in the complex plane. With this purpose a new concept of meromorphic factorization in the torus is introduced and discussed. The results...
Hausdorff dimension of functions on d-sets
2012-05-11
Speaker: António Caetano (Univ. Aveiro)
The sharp upper bound for the Hausdorff dimension of the graphs of the functions in Holder and Besov spaces (in this case with integrability p\geq 1) on fractal d-sets is obtained: \min\{d+1-s,d/s\}, where s\in(0,1] denotes the smoothness parameter. In particular, when passing from d\geq s...
Existence results for non-Newtonian viscous fluid problems with different types of dissipation
2012-04-27
Speaker:
Hermenegildo Borges de Oliveira (Univ. Algarve/CMAF)
This seminar aims to investigate the existence of weak and very weak solutions for generalized Navier-Stokes problems. We will consider different problems that govern distinct flows of incompressible and homogeneous viscous fluids. The analysis will be made mainly for the versions of...
On polynomial sequences associated to the classical linear functionals and to second order forms
2012-04-13
Speaker: Ana Filipa Loureiro (CMUP)
Polynomial sequences generated by integral powers of first and second order differential operators with polynomial coefficients will be under discussion. More precisely, the focus will lie on their connection with well known orthogonal polynomial sequences along with their foremost...
Non-smooth atomic decompositions in function spaces and applications
2012-03-30
Speaker: Cornelia Schneider (Univ. Erlangen-Nuremberg, Germany)
We provide non-smooth atomic decompositions for Besov spaces \Bd(\rn), s>0, 0<p,q\leq \infty, defined via differences, with the help of a homogeneity property.The results are used to compute the trace of Besov spaces on the boundary \Gamma of bounded Lipschitz domains \Omega with...
Spectral properties of certain tridiagonal k-Toeplitz matrices
2012-03-16
Speaker: Renato Álvarez-Nodarse (Univ. Sevilla, Spain)
Motivated by a physical model of a system of quantum oscillators with nonlinear interactions, we study spectral properties of certain matrices which arise as perturbations of some tridiagonal k-Toeplitz matrices. Concretely, we are interested in the spectral properties of...
Optimal partition problems involving Laplacian eigenvalues
2012-03-09
Speaker: Hugo Tavares (CMAF, Univ. Lisboa)
Given a bounded domain \Omega\subseteq \RN, N\geq 2, and a positive integer m\in \N, consider the following optimal partition problem \inf{ \sum_{i=1}^m \lambdak(\omegai): \omegai \subset \Omega open \forall i, \omegai\cap \omegaj=\emptyset whenever i\neq j},where \lambdak(\omega)...
Quantization in complex analysis and operator theory
2012-02-17
Speaker: Nelson Faustino (CMUC)
In this talk it will be explored the relevance of quantization on the construction of polyanalytic function spaces likewise its relevance on the study of class of Toeplitz operators obtained from Berezin quantization. Starting from a group representation for the Heisenberg group...
Global dissipative solutions of a coupled problem for image restoration
2012-01-20
Speaker:
Dmitry Vorotnikov (CMUC)
We consider a coupled nonlinear PDE model for image restoration. Both image and edge variables are incorporated by coupling them into two different PDEs. The features of our problem which oppose strong and classical weak well-posedness are the presence of a nonlinear function (modulus) of...
The weighted Stieltjes inequality and application
2011-06-17
Speaker:
Amiran Gogatishvili (Institute of Mathematics of the Czech Academy of Sciences, Czech Republic)
Let $1<p\leq q<\infty$. Inspired by some results concerning characterization of weighted Hardy type inequalities, where the equivalence of four scales of integral conditions was proved, we use related ideas to find some new equivalent scales of integral conditions related to the...
Optimal embeddings of spaces of generalized smoothness in the critical case
2011-04-08
Speaker: Cornelia Schneider (University of Erlangen, Nuremberg)
TBA...
Euclidean, hyperbolic and spherical geometries in the Landau equation with magnetic field
2011-04-01
Speaker: Zouhair Mouayn (Sultan Moulay University, Morroco)
We review the definition and properties of coherent states, their fundamental role in quantum mechanics as well as their most known generalizations with examples. We focus on the Gilmore-Perelomov approach in constructing coherent state by means of the representation theory of Lie groups and...
Problemas de cavidade totalmente não-lineares
2011-03-25
Speaker:
Eduardo Teixeira (Universidade Federal do Ceará, Brasil)
Dado um aberto O de Rn e uma função f \ge 0 na fronteira de O, um questionamento fundamental em matemática aplicada refere-se à solução do seguinte problema de fronteira livre: \Delta u = 0 ~ {u> 0\}, \quad u = f ~ \partial O, u_\nu = 1 ~\partial...
The Riemann-Hilbert method and the limit behavior of the reproducing kernels
2011-02-23
Speaker: Vitor Sousa (CIDMA, Aveiro)
TBA...
Well-posedness of dynamics of microstructure in solids
2010-11-26
Speaker:
Yasemin Sengul (CMUC)
This talk will be on the problem of well-posedness of nonlinear viscoelasticity under the assumptions allowing for phase transformations in solids. In one space dimension existence and uniqueness of the solutions for the quasistatic version of the model is proved by means of approximating...
Mathematics Training and Talent Search Programme
2010-10-18
Speaker: Ajit Kumar (Dep. Math., Inst. of Chemical Technology, Mumbai, India)
Mathematics Training and Talent Search Programme (M.T. & T.S.) is a national levelfour weeks intensive summer training programme in mathematics which has been runningsince 1993 in India. This programme is funded by the National Board for Higher Mathe-matics (NBHM) and is directed by S....
Landau's necessary conditions for the Hankel transform
2010-07-12
Speaker: Afonso Bandeira (DMUC)
We will prove Landau-type necessary density conditions for sampling and interpolation on spaces of functions whose Hankel transform is supported in a measurable subset $S$ of the positive semi-axis, in particular we prove the existence of an optimal Nyquist rate. As a special case, necessary...
Quasilinear singular equations
2010-07-07
Speaker: Tommaso Leonori (University of Granada, Spain)
TBA...
Regularized models for strongly nonlinear internal solitary waves
2010-06-25
Speaker: Ricardo Barros (BCAM, Bilbao, Spain)
We consider strongly nonlinear long wave models for large amplitude internal waves in two-layer flows. Both rigid-lid and free-surface are set for the upper boundary. It is shown that these models suffer from Kelvin-Helmholtz (KH) instability so that any given shear (even if arbitrarily...
Poly-Bergman spaces on domains Möbius equivalent to a disk
2010-06-18
Speaker: Luis V. Pessoa (IST, Lisbon)
Let $U$ be a complex domain Möbius equivalent to a disk and let $j$ be a non zero integer. The talk will focus on explicit representation of the poly-Bergman projection of order $j$ in terms of the canonical two-dimensional singular integral operators. One also shows how the Lebesgue...
Limits of inhomogeneous problems related to the p(x)-Laplacian
2010-05-28
Speaker: Mayte Perez-Llanos (IST, Lisbon)
Abstract...
The voice transform of the Blascke group generated by a representation on the weighted Bergman spaces
2010-05-14
Speaker: Margit Pap (Univ. Pécs, Hungary)
In this talk are presented results connected to the voice transform of the Blaschke group generated a representation of the group on the weighted Bergman spaces {\cal{H}}^m(\Bbb D). We give a representation U_a of Blaschke group on the weighted Bergman spaces {\cal{H}}^m(\Bbb D), we compute...
Bernstein estimates for systems of weakly coupled fully non-linear elliptic equations and integral operators
2010-04-09
Speaker: Gabrielle Terrone (IST, Lisbon)
Bernstein estimates permit to bound the sup-norm of the gradient of the solution with the sup-norm of the solution. We are particularly interested in systems that arise in the stochastic optimal control problems of hybrid systems, that are systems of weakly coupled nonlinear elliptic...
Non convex Aubry-Mather measures
2010-04-09
Speaker: Filippo Cagnetti (IST, Lisbon)
Given a smooth Hamiltonian H, we study the existence of measures invariant under the Hamiltonian flow, when H is non-convex. To simplify the treatment, we restrict ourselves to the periodic setting. Due to the lack of convexity, it is not possible to pass to the Lagrangian formulation, and...
Local well-posedness for generalized KP-II type equations on cylinders
2010-03-19
Speaker: Jorge Drumond Silva (IST, Lisboa)
We present recent results for the KP-II equations with generalized dispersion terms, in two and three spacial dimensions, periodic only in the x variable. We will start by showing how the solutions to the linearized equations satisfy bilinear Strichartz-type estimates, which are independent...
Nonlinear elliptic problems for a class of anisotropic operators
2009-12-11
Speaker: Agnese Di Castro (CMUC)
We present some existence and regularity results for nonlinear elliptic problems associated to a class of anisotropic operators, whose model is the anisotropic p-Laplacian. The results hold in a bounded domain and for Dirichlet boundary conditions....
Traces in Besov spaces
2009-12-04
Speaker: Cornelia Schneider (CMUC)
We investigate Besov spaces with positive smoothness, obtained by different approaches. Using an equivalent atomic characterization for these spaces, we are able to study traces in different settings.The results we obtain are rather complete and extend the ones previously known to small...
Local properties of non-negative solutions to some doubly non-linear degenerate parabolic equations
2009-11-27
Speaker: Simona Fornaro (University of Pavia, Italy)
We study the local behavior of non–negative weak solutions of a wide class of doubly non-linear degenerate parabolic equations. We show, in particular, some lower pointwise estimates of such solutions in terms of suitable sub-potentials (dictated by the structure of the equation) and...
A fundamental theory of linear transforms and applications to inverse problems
2009-10-23
Speaker: Saburou Saitoh (Emeritus Professor of Gunma University, Japan, and University of Aveiro, Portugal)
In this lecture, I would like to introduce some fundamental theory for linear transforms in the framework of Hilbert spaces and its general applications with very concrete typical examples. The contents will be given by the following key words: Reproducing kernel, Pythagorean theorem,...
Muckenhoupt weighted function spaces of Besov and Triebel-Lizorkin type: embeddings, traces, and singularities
2009-10-09
Speaker: Dorothee D. Haroske (Friedrich-Schiller-Universität Jena, Germany)
...
On the equations of viscoelastic diffusion in polymers
2009-09-25
Speaker: Dmitry Vorotnikov (CMUC - Universidade de Coimbra)
We shall consider the system of PDEs which models the non-Fickian anomalous (viscoelastic) diffusion of a penetrant liquid in a polymer. Recent results on existence, uniqueness and attractors for various types of generalized solutions to the corresponding boundary value problems will be...
Dynamics of linear operators
2009-06-17
Speaker: Özgür Martin (Bowling Green State University, Ohio, USA)
An intriguing result of G. D. Birkhoff states that there exists an entire function $f$ whose translates $f(z+n), n ≥0$ can approximate any entire function, uniformly on compacts sets. In 1952, as a similar result, G. R. MacLane showed existence of an entire function whose derivatives form...
Function spaces and Hausdorff dimension on fractals
2009-06-05
Speaker: António Caetano (Univ. Aveiro)
We start by recalling that, in the case of Sobolev spaces and Besov spaces on Rn, the Hausdorff dimension for the graphs of continuous functions belonging to such spaces has been studied by several authors, and that in the case of Besov spaces the final answer concerning the maximal...
Discrete function theory and its relations with Wigner Quantum Systems
2009-05-22
Speaker: Nelson Faustino (Univ. Aveiro)
...
Analysis of an economic stochastic differential game with non-market interactions for N players and its finite element approximation
2009-02-27
Speaker: Jens Vogelgesang (University of Bonn, Germany)
See here in pdf format
Area(s): ...
Topics in time-frequency analysis
2009-01-30
Speaker: Qiuhui Shen (Universidade de Aveiro)
In the first part of this talk we will review some classic tools in time-frequency analysis, including the windowed Fourier transform, the wavelet transform and the Wigner distribution. Then we relate them to the adaptive time-frequency analysis method: the theory of Huang's Empirical Mode...
On the linearization principle for the evolution problem governed by the system of equations of a mixed type
2009-01-23
Speaker: V.A. Solonnikov (POMI-Russian Academy of Sciences, St.Petersburg)
See here in pdf format
Area(s): ...
Existence and nonexistence of solutions for singular quadratic quasilinear equations
2008-12-10
Speaker: Tommaso Leonori (CMUC)
I want to show a result of existence and nonexistence for equations whose model is
-\Delta u + |Du|^2/u^{\gamma} = f(x) , in \Omega
(P)
u\in H^1_0 (\Omega)
where f(x) is a smooth positive function, $\gamma0$. We prove the existence of an optimal \gamma for the existence of a...
Dirichlet problems with quadratic gradient lower order terms
2008-09-22
Speaker: Lucio Boccardo (University of Roma 1, "La Sapienza")
Area(s): ...
Some remarks on parabolic capacity with
applications to nonlinear evolution equations with measure data
2008-09-17
Speaker: Francesco Petitta (C.M.A. - University of Oslo)
We will consider nonlinear evolution
problems modeled on the p-Laplacian, with
right-hand side a measure with bounded variation and initial datum in L^1. We will try to emphasize the new difficulties (with respect to the elliptic case) arising from the use of parabolic capacity by showing...
Análisis numérico de un modelo de remodelación ósea
2008-04-23
Speaker: Rebeca Martinez, (Univ. Santiago de Compostela)
En este trabajo se estudia, desde el punto de vista numérico, el modelo de remodelación ósea propuesto por Cowin y Hegedus (véase [1]). Este modelo se
caracteriza por una ecuación variacional elíptica para el campo de desplazamientos y una ecuación diferencial ordinaria de primer orden en...
Nonlinear eigenvalues for anisotropic quasilinear degenerate elliptic equations
2008-02-15
Speaker: Agnese Di Castro (University of Rome "La Sapienza")
I will speak about recent results obtained in collaboration with Eugenio Montefusco of the University of Rome "La Sapienza". We study the questions of existence, nonexistence and multiplicity of positive solutions for a class of anisotropic quasilinear elliptic equations with Dirichlet...
Wavelets: From the real line to the unit sphere
2008-02-01
Speaker: Milton Ferreira (Instituto Politécnico de Leiria)
Wavelet theory is applicable to several subjects and fields of science. All wavelet transforms may be considered forms of
time-frequency representation for continuous-time (analog) signals and so are related to harmonic analysis.
A wavelet is a kind of mathematical function used to divide...
Sobre as propriedades algébricas, diferenciais, integrais e espectrais dos núcleos do tipo Mercer
2007-12-07
Speaker: António Paixão (Departamento de Engenharia Mecânica, ISEL, Lisboa)
Apresentam-se resultados recentes sobre os núcleos (ditos do tipo Mercer) de certos operadores integrais positivos, com ênfase no caso em que estes estão definidos em intervalos ilimitados de R e adquirem significado no contexto da transformação de Fourier.
Estes resultados surgem como...
The Space Formed by Special Atoms: Origin, Motivations, Generalizations and Applications
2007-10-26
Speaker: Geraldo de Souza (Auburn University)
Area(s): ...
Large solutions for a class of nonlinear elliptic equations with gradient terms
2007-10-12
Speaker: Tommaso Leonori (CMUC)
See here in pdf format
Area(s): ...
Numerical analysis of some contact problems involving piezoelectricity
2007-06-01
Speaker: José Ramon Fernández García (Universidade de Santiago de Compostela)
In this talk, two contact problems will be presented. The first one
concerns an elastic body in contact with a rigid or deformable
obstacle, and the second one deals with the contact of a viscoelastic
body with a deformable foundation. In both cases, piezoelectric
effects are taken...
Frames
2007-02-07
Speaker: Luís Daniel Moura de Abreu (DMUC e CMUC, Univ. de Coimbra)
Uma base de um espaço vectorial com produto interno é um conjunto gerador minimal desse espaço.Um Frame de um espaço vectorial com produto interno é um conjunto gerador, mas não necessariamente minimal, e que pode ser definido através de uma...
On the problem of stability of equilibrium figures of uniformly rotating liquids
2007-01-09
Speaker: Vsovolod A. Solonnikov
(Univ. of Ferrara, Italy, and Steklov Mathematical Institute, St.Petersburg, Russia)
We analyze the stability of some special solutions of the free boundary
problem governing the evolution of an isolated mass of a viscous
incompressible self-gravitating liquid. We briefly describe the results
with surface tension and we give special attention to recent results in the...
Teoria de Klainerman-Majda e Aplicações
2006-11-24
Speaker: Filipe Oliveira (Univ. Nova de Lisboa)
A teoria de Klainerman-Majda (1981) permite descrever o comportamento das soluções de alguns sistemas hiperbólicos semi-lineares quando certos parâmetros tendem para zero. ?? o caso por exemplo dos limites incompressiveis das equações de Navier-Stokes e de Euler, obtidos num certo sentido a...
Evolution unilateral contact problems with adhesion and friction in (visco)elasticity.
2006-10-13
Speaker: Marius Cocou (LMA - CNRS and Université de Provence, Marseille, France)
My talk concerns an analysis of two classes of unilateral contact problem with adhesion and friction between two (visco)elastic bodies.
First, I present a quasistatic contact problem with Signorini conditions, adhesion and local Coulomb friction for two elastic bodies.
Second, I consider...
On Weighted Estimates for the Averaging Integral Operator
2006-09-22
Speaker: Bohumir Opic (Math. Institute/Academy of Sciences of the Czech Republic)
See here in pdf format
Let $1 Area(s): ...
A dynamical systems approach to understanding deep brain stimulation
2006-09-06
Speaker: Jonathan Rubin (Univ. Pittsburgh, USA)
Deep brain stimulation (DBS) is a surgical intervention in which an electrode is implanted in a localized area of a patient's brain, where it delivers high-frequency electric current pulses. This technique has proved particularly effective at tremor suppresion and thus has been implemented...
Weyl number methods for the investigation of spectral
asymptotics of matrix and integral operators
2006-05-26
Speaker: Aicke Hinrichs (Fac. Mathematics and Computer Science, Univ. Jena, Germany)
We give an overview of methods for the determination of the
asymptotic behavior of the eigenvalue sequence of bounded
linear operators in Banach spaces. Particular emphasis will
be put on estimates of eigenvalues via Weyl numbers in
contrast to the more often used entropy numbers....
Shape generalization of digital elevation models
2006-05-12
Speaker: Carsten Ebmeyer (University of Bonn)
The most common form of digital representations of topographic surfaces are Digital Elevation Models (DEMs) consisting of points of elevations, sampled systematically at equally spaced grids. The main focus of my talk is to investigate anisotropic diffusion models in form generalisation....
Function Spaces with Muckenhoupt weights and related Trace Problems on Fractals
2006-05-05
Speaker: Iwona Piotrowska (Univ. Jena, Germany)
In the first part of this talk we discuss an atomic decomposition of Besov and Triebel-Lizorkin spaces with Muckenhoupt weights. We improve a result of S. Roudenko on matrix-weighted Besov spaces byproving an atomic decomposition also in the case
0
The second purpose of this talk is...
The Art and Science of Achieving Harmonics on Stringed Instruments
2006-04-05
Speaker: Steven J. Cox (Computational and Applied Mathematics, Rice University)
One may elicit the qth tone of a string by applying the `correct touch' at one of its q-1 nodes during a simultaneous pluck or bow. This effect was first scored for violin by Mondonville in 1735. Though it captured the attention of the 19th century masters,
Chladni, Tyndall, Helmholtz and...
Growth envelopes of anisotropic function spaces
2006-03-24
Speaker: Mariusz Piotrowski (CMUC/U. Coimbra)
We consider growth envelopes of anisotropic spaces of Besov and Triebel-Lozorking type.
Additionally, we describe anisotropic Hardy inequalities in these spaces. Area(s): ...
Computational aspects in the analysis of composite,
sandwich and functionally graded laminates
2006-03-10
Speaker: António Joaquim Mendes Ferreira (Dep. Eng. Mecânica e Gestão Industrial, FEUP)
In this talk the author introduces its research activity in
computational models for the analysis of composite, sandwich and
functionally graded laminated plates and beams. Recent advances in
radial basis functions and combinations with pseudospectral methods
are presented....
Entropy solutions for the p(x)-Laplace equation
2006-03-03
Speaker: Manel Sanchón (CMUC, Univ. Coimbra)
We consider a Dirichlet problem in divergence form with variable
growth, modeled on the p(x)-Laplace equation. We obtain existence and
uniqueness of an entropy solution for L^1 data, extending a work of Bénilan
et al. to nonconstant exponents, as well as integrability results for...
Fractal geometry and smoothness on
Besov-Triebel-Lizorkin spaces and Weierstrass-type functions
2006-01-27
Speaker: José Abel Lima Carvalho (Functional Analysis and Appl. Group, U. Aveiro)
Fourier analysis and the Theory of Function Spaces are closely connected with several aspects of fractal geometry.
We want to relate three different forms of
measuring smoothness on the class of all
continuous real functions with compact support:
Frequency structure in the...
Mathematical models in Biology: Two way street
2006-01-06
Speaker: Renato Álvarez-Nodarse
(Dpto. Analisis Matematico, Univ. de Sevilla)
The aim of this talk is to show the useful connection between mathematics and biology. There is a two way street. In one way, the use of mathematical models helps us to quantitative understand biological and medical problems, and on the other, modelizing biological systems leads to very...
Instability of saddle solutions of semilinear elliptic equations
2005-12-02
Speaker: Joana Terra
(Universitat Politecnica de Catalunya)
In a joint work with Xavier Cabre, we study the instability properties of some saddle solutions of the semilinear elliptic equations $-\Delta u=u-u^3$ in the whole $\R^{2m}$.
In 1995 M. Schatzman proved that in dimension $2$ there exists a saddle solution and it is unstable.
We prove...
Semi-stable and extremal solutions of reaction equations involving the
p-Laplacian
2005-11-25
Speaker: Manuel Sanchón (CMUC/Univ. Coimbra)
We consider nonnegative solutions of $-\Delta_p u=f(x,u)$, where
$p1$ and $\Delta_p$ is the $p$-Laplace operator, in a
smooth bounded domain of $\mathbb{R}^N$ with zero Dirichlet boundary
conditions. We introduce the notion of semi-stability for a
solution $u$, and we give examples and...
Vector Valued Fourier Transforms and Fourier Type
2005-11-18
Speaker: Mariusz Piotrowski (CMUC/U. Coimbra)
The central question of this talk is whether the methods of
scalar-valued harmonic analysis can be transferred to the
vector-valued setting. Fortunately, the answer of this question is
negative. This opens the opportunity to classify Banach spaces (or
operators) by measuring how well ...
Efeitos de curvatura e de torção em guias de onda unidimensionais
2005-11-11
Speaker: Luís Trabucho (CMAF/Univ. Lisboa)
Considerando a equação de Schrödinger para uma partícula confinada a mover-se numa dada região tubular, os diversos níveis de energia e as respectivas funções de onda são solução de um problema de valores e de vectores próprios para o operador de Laplace.
Neste trabalho, utilizando técnicas...
Sistemas diferenciais de 1a. ordem que
generalizam a equação de Cauchy-Riemann da Análise de Clifford
2005-10-28
Speaker: Gil Bernardes (CMUC/U. Coimbra)
Em Análise de Clifford clássica estudam-se soluções, de $n$
variáveis reais, de um sistema de 1a. ordem que pode escrever-se
como uma única equação se permitirmos que os coeficientes e as
soluções possam tomar valores numa Álgebra de Clifford de
dimensão $2^n$.
Para o sistema...
Regularidade para EDPs com uma não-linearidade de tipo
exponencial
2005-07-15
Speaker: Eurica Henriques (CMUC/Universidade de Trás-os-Montes e Alto Douro)
Consideram-se equações fortemente degeneradas na forma
$$ \partial_t u - \nabla \cdot ( |u|^{\gamma(x,t)} \nabla u )= f \ ,$$
em que a não-linearidade é do tipo exponencial.
Para hipóteses naturais sobre os dados, é obtida a continuidade local
das soluções fracas da equação. Area(s): ...
A reaction-diffusion system modeling the cardiac electric field
2005-07-15
Speaker: Mostafa Bendahmane (University of Oslo, Norway)
We are concerned with a degenerate system of nonlinear
partial differential
equations modeling the cardiac electric field at macroscopic level.
First, the existence of weak solutions is proved via non degenerate
approximation
system, Faedo-Galerkin, monotonicity and compactness...
Algoritmos Evolucionários em Optimização Uniobjectivo e Multiobjectivo: Aplicação à Optimização de Placas
2005-06-17
Speaker: Lino Costa ( Dep. de Produção e Sistemas, Univ. do Minho)
Os algoritmos evolucionários (AEs) têm sido aplicados na optimização de diversos problemas de engenharia. Estas abordagens apresentam como principal desvantagem tempos de computação elevados mas, por outro lado, exibem uma grande flexibilidade na modelação dos problemas. Por outro lado,...
Algebraic and continuous properties of multilinear forms
2005-06-03
Speaker: Richard M. Aron (Kent State University, USA)
Let $X$ be a vector space and let $\phi, \psi \in X^\ast$ be two
linear forms on $X.$ It is well known that if, for any $x \in X, $
$$\phi(x) = 0 \Rightarrow \psi(x) = 0,$$
then $\psi = c \phi$ for some scalar $c.$ A continuous version is
also known. Namely, if $X$ has a...
Soluções fracas para EDP não-lineares e limites de relaxação.
2005-04-22
Speaker: Manuel Portilheiro (CMUC/Universidade de Coimbra)
?? possível estabelecer um enquadramento abstracto de solução fraca
do qual são casos especiais as soluções de entropia de Kruzhkov para as
leis de conservação e as soluções de viscosidade para as equções de
Hamilton-Jacobi. Esta formulação tem também interesse a nível práctico,
sendo...
Princípios da incerteza para transformadas integrais.
2005-03-11
Speaker: Luís Daniel Abreu (Universidade de Coimbra)
Um princípio da incerteza para uma transformada integral é um teorema que,
nas palavras de Norbert Wiener, revela a impossibilidade de uma função e a
sua transformada serem simultaneamente pequenas. Os princípios da incerteza
relacionados com a transformada de Fourier, foram...
Diferenciabilidade cónica da solução dum problema de contacto
2005-02-11
Speaker: Cecília Maria M. A. Soares Pinto (Escola Superior de Tecnologia de Viseu, IPV)
Nesta apresentação iremos considerar uma viga que por acção de forças aplicadas pode entrar em contacto com um obstáculo.
A secção da viga é perturbada através dum pequeno parâmetro que altera a forma da viga.
Usando um modelo de remodelação óssea estabelecido por [1] , em que o...
Convergência de conjuntos convexos com restrição no gradiente.
2004-12-03
Speaker: Lisa Santos (Universidade do Minho)
See here in pdf format
Area(s): ...
Polinómios ortogonais semi-clássicos com suporte numa circunferência
2004-10-22
Speaker: Amilcar Branquinho (CMUC/Universidade de Coimbra)
Estabeleceremos a teoria geral das sucessões de
polinómios ortogonais com suporte numa circunferência.
Daremos algumas proprieadades que
caracterizam as famílias semi-clássicas, bem
como alguns exemplos destas sucessões.
Area(s): ...
Entropy numbers of embeddings of weighted Besov spaces. The limiting case.
2004-09-24
Speaker: Hans-Gerd Leopold (Friedrich-Schiller-University of Jena/Germany)
See here in pdf format
The talk presents results of joint work with T.KÌhn (Leipzig), W. Sickel (Jena) and L. Skrzypczak (Poznan).
We investigate the asymptotic behaviour of the entropy numbers of the
compact embedding
id:B^{s_1}_{p_1,q_1}(\R^d, w) -----...
Ceros de polinomios extremales no standard en el plano complejo
2004-06-18
Speaker: Ignacio Perez Izquierdo(Universidade Carlos III, Madrid)
Bajo ciertas condiciones, se prueba que los ceros de una
sucesion de polinomios extremales con respecto a una norma no standard,
estan acotados. Tambin se estudia la distribucion asimptotica de dichos
ceros. Area(s): ...
Sobolev spaces of generalised smoothness and sub-Markovian semigroups
2004-05-14
Speaker: Erich Walter Farkas (Swiss Banking Institute/University of Zurich)
It is cornerstone in the thory of modern theory of stochastic processes that to each (regular) Dirichlet form one can associate a stochastic process. From the probabilistic point of view
there is a disadvantage to work with processes associated with
Dirichlet spaces because the process is...
Optimização de forma para um modelo de viga
2004-04-30
Speaker: Isabel M. Narra de Figueiredo
Area(s): ...
Modelos Matemáticos para o Movimento Celular
2004-04-02
Speaker: Fabio Chalub (CMAF/Universidade de Lisboa)
O estudo do movimento celular tem muitas aplicações, desde a imunologia (quando células devem migrar da corrente sanguínea para o local da infecção), embriologia (onde cada célula deve encontrar seu local correto) e muitos outros.
Neste seminário mostraremos o modelo de Keller-Segel,...
O Problema das N-membranas para sistemas degenerados não-lineares
2004-03-12
Speaker: José Francisco Rodrigues (Universidade de Lisboa)
We consider the elliptic variational inequality associated with quasilinear
nonlinear
systems, including those of p-Laplacian type, and with the ordering
constraint of the
N-membrane problem. We extend the Lewy-Stampacchia inequalities for the
solution,
obtaining new regularity...
Domínios nodais do Laplaciano
2004-03-05
Speaker: Pedro Freitas (Instituto Superior Técnico)
?? excepção do teorema de Courant que diz que o número de
domínios
nodais de uma função própria do Laplaciano associada com o
k-ésimo
valor próprio é no máximo k, muito pouco é conhecido
sobre a estrutura
das funções próprias do Laplaciano. ...
Gamma function inequalities - a survey
2004-02-20
Speaker: Horst Alzer (Germany)
Area(s): ...
On p(x)-harmonic functions
2004-02-13
Speaker: V.V. Zhikov (Univ. Vladimir, Russia)
tba Area(s): ...
Logarithmic asymptotic of Sobolev orthogonal
polynomials
2004-02-13
Speaker: Hector E. Pijeira Cabrera (Universidad Carlos III de Madrid, Spain)
For a wide class of Sobolev inner product with support on
the real line, the logarithmic asymptotic of the
corresponding Sobolev orthogonal polynomials is given,
using logarithmic potential theory results.
Area(s): ...
Modelos para gases quimicamente activos sujeitos a efeitos dissipadores
2004-01-23
Speaker: Ana Jacinta Soares (Universidade do Minho)
No contexto da teoria cinética estendida a gases quimicamente activos,
consideram-se modelos em que as partículas do gás possuem velocidades pertencentes a um conjunto finito de vectores previamente fixado.
Ao nível microscópico, a evolução do gás é regida por um sistema
não linear de...
Operadores limitados em espaços de Triebel-Lizorkin
2004-01-16
Speaker: João Pedro Silva Brito Boto (CMAF/Universidade de Lisboa)
Dado um operador limitado $T:L^{p_{0}}\left( \mathbb{R}^{n}\right)
\rightarrow L^{p_{1}}\left( \mathbb{R}^{n}\right) $, para $1\leq
p_{0},p_{1}\leq \infty $, damos condições para que $T$ defina um
operador limitado entre pares correspondentes de espaços $L^{p}\left(...
Factorização e regularidade de operadores do tipo de convolução
2004-01-09
Speaker: Luís Castro (Universidade de Aveiro)
São estudados determinados operadores do tipo de convolução, actuando entre
espaços de potenciais de Bessel, sob o ponto de vista das suas propriedades
de regularidade (designadamente, a propriedade de Fredholm e a
invertibilidade). Para o efeito são introduzidos novos conceitos...
Amann problem for the system of parabolic-elliptic equations
2003-12-19
Speaker: Galina Bizhanova (Institute of Mathematics, Almaty, Kazakhstan)
Area(s): ...
Changing blow-up time in nonlinear Schrödinger equations
2003-12-05
Speaker: Rémi Carles (CNRS/Université de Rennes 1)
Solutions to nonlinear Schrödinger equations may blow up in finite
time. We study the influence of the introduction of a potential on this
phenomenon. For a linear potential (Stark effect), the blow-up time
remains unchanged, but the location of the collapse is altered. The main
part...
A Progress in the Theory of Lebesgue Spaces with Variable Exponent:
Singular Operators and Sobolev Theorem for Potentials
2003-11-28
Speaker: Stefan Samko (Universidade do Algarve)
The talk provides a discussion of recent results for the generalized
Lebesgue spaces with variable exponent p(x) (GLSVE) including some
results on boundedness of Hardy-Littlewood maximal operator and
criterion for the weighted singular operator (with a power weight) to be
bounded in...
Momento de flexão em teoria de membranas
2003-11-14
Speaker: Luísa Mascarenhas (CMAF/Universidade de Lisboa)
Estuda-se um modelo de membrana não linear na qual as forças externas
induzem uma densidade de momento de flexão. A justificação matemática deste
modelo é feita por passagem 3D-2D, via Gama-convergência.
(colaboração com G. Bouchitté e I. Fonseca) Area(s): ...
Inversão do operador potencial de Riesz nos espaços de Lebesgue de expoente variável
2003-10-31
Speaker: Alexandre Almeida (Universidade de Aveiro)
O comportamento do operador potencial de Riesz foi estudado recentemente no contexto dos espaços de Lebesgue de expoente variável, conduzindo à generalização de certos teoremas do tipo Sobolev. No seguimento de tais resultados, aborda-se o problema da inversão deste operador em tais espaços....
Uma q-versão do teorema de amostragem de Whittakker-Shannon-Koltenikov
2003-10-17
Speaker: Luís Daniel Abreu
O Teorema de amostragem de Whittaker-Shannon-Kotelnikov é um resultado
central da Análise Harmónica com aplicações importantes à Engenharia de Comunicações, nomeadamente na Teoria do Sinal, pois permite aos engenheiros reconstruir um dado sinal a partir das suas amostras num conjunto...
Low Mach number limit for polytropic compressible flows
2003-09-19
Speaker: Didier Bresch (Université Joseph-Fourier/CNRS, Grenoble, France)
This talk concerns the low Mach number limit for polytropic compressible flows. The goal is to show that we are far from being
able to get a complete mathematical asymptotic proof.
Neverthless we will give some recent partial answers to the subject.
Area(s): Partial Differential...
Extensions of Rodrigues' formula for second kind solutions of hypergeometric equation
2003-09-05
Speaker: Andre Ronveaux (University of Namur, Belgium)
Benjamin Olinde Rodrigues is well known for basic formula in the representation of orthogonal polynomials.
In this talk a quick summary of his life and social environment will be presented. Moreover, we shall introduce a representation of Rodrigues type for the Second Kind Functions of all...
O problema de Cauchy para equações de evolução não lineares dispersivas de tipo Schrödinger
2003-07-11
Speaker: Filipe Oliveira (Universidade do Minho)
Depois de passar em revista as diferentes propriedades de dispersão e regularização associadas ao grupo de Schrödinger ($L^p-L^q$, Strichartz, Kenig-Ponce-Vega), será feita uma
aplicação à resolução do problema de Cauchy (local e global) para o sistema de Zakharov-Rubenchick.
Este...
Index transforms associated with generalized hypergeometric functions
2003-06-13
Speaker: Semyon Yakubovich (Departamento de Matemática Pura, Faculdade de Ciências da Universidade do Porto)
We deal with a class of integral transformations whose kernels contain the Clausenian hypergeometric function. These transforms are defined in terms of integrals with respect to their parameters. It involves as particular cases the familiar Olevskii and generalized Mehler-Fock transforms...
Applications of PDEs to option pricing
2003-05-23
Speaker: Vincenzo Vespri (Universidade de Florença, Itália)
The pricing of European and American Options is ruled by the Black & Scholes equation. This equation is a parabolic linear PDE with degenerate and unbounded coefficients. In this talk we analyze this equation and its generalizations and study existence, uniqueness, positivity and convexity...
Aproximação de transformações conformes
2003-04-11
Speaker: Irene Falcão (Universidade do Minho)
Um dos aspectos mais importantes das transformações conformes é a invariância das soluções da equação de Laplace. Assim, as transformações conformes podem ser usadas em problemas de condução de calor, electroestática, hidrodinâmica e outras aplicações físicas onde a equação de Laplace...
Stability of equilibrium figures of a rotating fluid
2003-03-28
Speaker: V.A. Solonnikov (CMAF/Univ. Lisboa, POMI-Steklov Math Institute, St.Petersburg)
Area(s): ...
Modelos cinéticos de quimiotaxia
2003-03-21
Speaker: Fabio Chalub (University of Vienna, Austria)
Quimiotaxia é o estudo do movimento celular induzido pela presença de um gradiente químico. O modelo matemático mais importante de quimiotaxia foi apresentado por Keller e Segal na década de 70. Nesta palestra, após uma breve introdução ao modelo de Keller-Segel, apresentaremos um novo...
Polinomios Ortogonales Polares
2002-12-06
Speaker: Héctor E. Pijeira Cabrera, Universidad de Matanzas, Cuba
Area(s): ...
Envelope functions and approximation numbers: two examples
2002-10-09
Speaker: Dorothee D. Haroske, Jena, Germany
Area(s): ...
Weak continuity of nonlinear elliptic operators and applications
2002-07-10
Speaker: Neil Trudinger, Australian National University, Australia
Area(s): ...
Spectral theory of some fractal elliptic operators
2002-06-05
Speaker: Hans Triebel, Friedrich-Schiller-University Jena, Germany
Area(s): ...
On the interpolation constant for (sub)linear operators in Orlicz spaces
2002-05-17
Speaker: Alexei Karlovich, Instituto Superior Técnico
Area(s): ...
Convolution complementarity problems
2002-04-15
Speaker: David Stewart, University of Iowa, USA
Area(s): ...
Subspace optimization models and the graph partitioning problem
2002-04-15
Speaker: Suely Oliveira, University of Iowa, USA
Parallel data distribution can be modeled as a Graph Partitioning Problem where we wish to divide a graph into subgraphs with roughly equal number of nodes with a mininum number of edges crossing between the subgraphs. This is a well-known NP-complete problem so heuristics need to be...
Números $s$ de imersões de espaços logarítmicos em espaços de Zygmund generalizados
2002-02-01
Speaker: António Bento, Universidade da Beira Interior, Portugal
Area(s): ...
Espaços de potenciais de Bessel modelizados em espaços de Lorentz-Karamata e imersões (caso super-limite)
2001-12-14
Speaker: Júlio S. Neves, Universidade de Coimbra, Portugal
Area(s): ...
Interpolação de ideais de operadores
2001-12-07
Speaker: Pedro Matos, Instituto Politécnico de Leiria, Portugal
- Definições e resultados básicos de Teoria da Interpolação
- Resultados sobre a interpolação de operadores compactos
- Definição de medidas para ideais de operadores
- Resultados sobre interpolação de ideais de operadores
Area(s): ...
Harmonic Bergman spaces in the unit Ball
2001-11-30
Speaker: Guangbin Ren, Universidade de Aveiro, Portugal
Some basic techniques are established for the theory of harmonic Bergman space. For example, the hypergeometric functions are expressed as the integral of generating functions of Gegenbauer polynomials, so that we can obtain the precise form of the Forelli-Rudin type estimation for the power...
Envelopes in function spaces
2001-10-03
Speaker: Dorothee D. Haroske, Jena, Germany
Area(s): ...
On the Saponjyan paradox in the theory of thin plates
2001-07-13
Speaker: Serguei Nazarov, St. Petersburg University, Russia
Taking a problem on bending of simply-supported polygonal Kirchoff plate as an example, it is shown that a reformulation of the boundary-value problem in terms of potentials may lead to a complete change in the solution. An approach based on self-adjoint extensions of operators can improve...
Integral transforms and q-polynomials
2001-07-11
Speaker: Renato Alvarez-Nodarse, University of Sevilla, Spain
It is well known the importance of the integral transforms and special functions in several areas of Mathematical and Physical Sciences. In fact, a deep knowledge of the Special Function Theory allows us to solve several problems in quantum and classic Mechanics, non-linear equations, etc....
Integral transformations of the Kontorovich-Lebedev type
2001-07-06
Speaker: Semyon Yakubovich, Universidade do Porto, Portugal
A survey talk about recently published results in the Lp-theory of integral operators associated with special functions of the hypergeometric type as kernels is presented. The theory of the Mellin and the Kontorovich-Lebedev transformations is applied in order to prove related results for...
A new characterization of classical forms
2001-06-01
Speaker: Pascal Maroni, University of Paris VI, France
We show that an orthogonal polynomial sequence, whose m-th associated sequence of k-th derivative sequence is orthogonal, is necessarily a classical one. When m=0, it is the Hahn's theorem.
Area(s): ...
Gamma, digamma, polygamma functions - and an inequality of J.S. Martins
2001-05-18
Speaker: Horst Alzer
We give a survey talk on some recently published mean value inequalities for the classical gamma function, the digamma function and the polygamma functions. Further, we provide inequalities for the arithmetic, geometric, and harmonic means of the first n positive integers. These mean values...
Valores próprios minimais para operadores de Scrödinger em variedades compactas
2001-05-11
Speaker: Pedro Freitas, Instituto Superior Técnico, Portugal
Considera-se o problema de minimizar os valores próprios do operador de Scrödinger $H=-\Delta+\alpha \ka^{2}$ ($\alpha0$) numa variedade compacta quando a média de $\ka$ é fixa. Em dimensão um, prova-se que o potencial constante deixa de ser minimizante a partir de um valor crítico do...
On some fractional evolution equations
2001-04-27
Speaker: Stig-Olof Londen, Helsinki University of Technology, Finland
In this talk, we review some recent results on fractional evolution equations of type
$$D_{t}^{\alpha} u+A u=f, \quad t\geq 0,$$ where $\alpha \in (0,2)$, $\alpha \neq 1$. First, as a typical example, we consider the fractional Burgers equation. Next, we formulate a general result with $A$...
Difracção de ondas sob uma perspectiva da teoria de operadores
2001-04-06
Speaker: Luís Filipe Castro, Universidade de Aveiro, Portugal
Uma classe de problemas da teoria da difracção, possuindo ligações aos problemas clássicos de Sommerfeld, é analisada sob a perspectiva da teoria de operadores. Tal significa que após uma formulação inicial do problema por via da equação de Helmholtz e de condições de fronteira, este é...
On function spaces of generalized smoothness
2001-03-30
Speaker: Hans-Gerd Leopold, University of Jena, Germany
Function spaces of generalized smoothness have been introduced and considered from different points of view - characterisation by approximation, interpolation, operators, differences. This have been done by a variety of authors particularly since the middle of the Seventies up to the end of...
Dinâmica caótica: o ponto de vista probabilístico
2001-03-23
Speaker: José Ferreira Alves, Universidade do Porto, Portugal
Em Sistemas Dinâmicos procura-se entender a evolução de sistemas cujo estado se altera ao longo do tempo, tentando prever a sua evolução. Tem-se constatado que um grande número de sistemas se comportam de forma caótica: os estados futuros do sistema são muito afectados por pequenas variações...
Weak continuity of nonlinear elliptic operators and applications
2001-03-10
Speaker: Neil Trudinger, Australian National University, Australia
Area(s): ...
Variational and quasi-variational inequalities for critical-state models in plasticity and superconductivity
2001-03-10
Speaker: José Francisco Rodrigues, Universidade de Lisboa, Portugal
Area(s): ...
Análise de sensibilidades de placa sujeita a obstáculo
2001-01-19
Speaker: Carlos Leal, Universidade de Coimbra, Portugal
We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results for the linear case, is done by application of an abstract variational result, where the...
Imersões limite dos espacos de Sobolev (fraccionários) modelizados em espaços de Lorentz-Karamata
2001-01-05
Speaker: Júlio Neves, Universidade de Coimbra, Portugal and University of Sussex, UK
Vamos considerar espaços de Sobolev (fraccionários), modelizados em espaços de Lorentz-Karamata e apresentaremos imersões limite destes espaços em espaços de Lorentz-Karamata e em espaços de Orlicz. Estes resultados estão relacionados com as imersões de Peetre-Strichartz-Trudinger e...
Existence of solutions of a non linear cross diffusion system arising in population dynamics
2000-12-15
Speaker: Gonzalo Galiano, Universidad de Oviedo, Spain
We present results on existence of solutions for a strongly coupled cross-diffusion model for two competing species based on a semidiscretization in time. The variables are the population densities of the species. Existence of strictly positive weak solutions to the semidiscrete problem is...
The porous medium equation: a model of a free boundary with a finite speed of propagation
2000-11-24
Speaker: Carsten Ebmeyer, University of Bonn, Germany
The porous medium equation is a degenerate parabolic differential equation. It is used in modelling free boundaries with a finite speed of propagation. At the free boundary the solution may be singular. The aim of this talk is to discuss the regularity of weak solutions and its behaviour...
q-análogos de funções trigonométricas numa rede q-linear. Propriedades dos zeros. Construção de q-Séries de Fourier.
2000-10-13
Speaker: José Luís Cardoso, Universidade de Trás-os-Montes e Alto Douro, Portugal
Breve construção de q-análogos de funções trigonométricas como soluções de equações de diferenças. Definição de redes q-lineares e de redes q-quadráticas. Escrita daquelas soluções na forma de séries hipergeométricas básicas. Definição de q-Integral e $\delta$-Diferenciação....
Algebraic and order completion methods in solving nonlinear PDEs, parametric global Lie group actions and solutions to Hilbert's fifth problem
2000-09-22
Speaker: Elemér E. Rosinger, University of Pretoria, South Africa
The talk is a survey of the work of the speaker and a few collaborators published in a number of books and papers. The presentation is focused on the basic ideas and results, without going into technical detail, thus it is accessible to a general mathematical audience. 1. The algebraic...
A sensitivity and adjoint calculus for the optimal control of flows with shocks
2000-09-15
Speaker: Stefan Ulbrich, Technische Universitat Munchen, Germany
Optimal control or design problems for hyperbolic conservation laws arise for example in the design of ducts and airfoils or in the identification of friction parameters in shallow water flows after neglecting viscous effects. A key point for an efficient solution of the resulting...
Padé approximants and orthogonal polynomials
2000-09-13
Speaker: Bernardo de la Calle Ysern, Universidad Politécnica de Madrid, Spain
Padé approximants are rational functions which may be seen as a generalization of Taylor polynomials. In this lecture, basic facts and main classical theorems on convergence theory of Padé approximants to analytic functions are briefly reviewed. We show the important role played by...
Uniform and Hölder approximation
2000-06-23
Speaker: Miguel A. Jimenez, Benemerita Universidad Autonoma de Puebla, Mexico
Many results that appear in dealing with best Chebyshev approximation by algebraic or trigonometric polynomials have been extended to Hölder polynomial approximation. However it is clear that uniform convergence is a necessary but not a sufficient condition for Hölder approximation. We...
Nonlinear elliptic equations on non-smooth domains under mixed boundary value conditions
2000-06-16
Speaker: Carsten Ebmeyer, University of Bonn, Germany
Nonlinear elliptic problems are considered under mixed Dirichlet-Neumann boundary conditions. It is assumed that the domain $\Omega$ has a piecewise smooth boundary (e.g. the domain is a polyhedron). Using a difference quotient technique, we get regularity results for weak solutions in...
Weak solutions for a class of non-Newtonian fluids with energy transfer
2000-06-09
Speaker: Luísa Consiglieri, CMAF, Universidade de Lisboa, Portugal
We shall consider a nonlinear thermoconvection problem consisting of a coupled system of nonlinear partial differential equations due to temperature dependent coefficients. We prove that weak solutions exist in appropriate Sobolev spaces under mild hypothesis on the regularity of the data....
The polynomial property of elliptic problems and an algebraic description of their attributes
2000-05-19
Speaker: Serguei Nazarov, St. Petersburg University, Russia
The polynomial property of a self-adjoint system of differential operators means that the corresponding sesquilinear form degenerates on a finite-dimensional subspace of polynomials only. Almost all stationary problems in mathematical physics provide an example of such a system. In the...
Solutions of fully nonlinear equations with patches of zero gradient: existence, regularity and convexity of level curves
2000-05-05
Speaker: Jorge Salazar, CMAF, Universidade de Lisboa, Portugal
In this talk (a joint work with Luis Caffarelli), we are going to report on the construction of viscosity solutions (in the Crandall-Lions sense) of fully nonlinear equations of the form $F(D^2 u,x) = g(x,u)$ on $\{|\nabla u| \ne 0$. By an appropiate use of the Alexandroff-Backelmann...
Espaços de funções de parâmetro de derivação generalizado
2000-04-07
Speaker: Susana Domingues de Moura, Universidade de Coimbra, Portugal
Os espaços de funções que abordaremos generalizam os espaços de Besov e Triebel-Lizorkin. Apresentaremos algumas propriedades dos referidos espaços, nomeadamente caracterizações via decomposições atómicas e subatómicas.
Area(s): ...
Aproximação racional e polinómios ortogonais
2000-03-24
Speaker: Guillermo López Lagomasino, Universidad Carlos III de Madrid, Spain
Existe uma relação estreita entre propriedades assimptóticas de sucessões de polinómios ortogonais e a convergência de aproximantes racionais a funções meromorfas. Veremos como esta relação é mutuamente proveitosa às duas teorias.
Area(s): ...
Extensão de um resultado de Gomes Teixeira
2000-03-10
Speaker: Amílcar Branquinho, Universidade de Coimbra, Portugal
Vamos apresentar um resultado de Gomes Teixeira que permite obter de uma forma unificada a função geradora das famílias de polinómios ortogonais clássicas. Da mesma forma veremos como estender este resultado obtendo funções geradoras de algumas famílias de polinómios ortogonais de várias...
Um problema não linear de duas membranas
2000-02-25
Speaker: Lisa Santos, Universidade do Minho, Portugal
Demonstra-se existência e regularidade de solução para um problema de duas membranas com diferentes coeficientes de elasticidade. O resultado para o problema linearizado está estabelecido na literatura. No caso não linear, para garantir existência de solução, é necessrio impÎr uma condição...
Asymptotic conditions at infinity for the Stokes problem in a system of pipes
2000-02-11
Speaker: Konstantin Pileckas, Vilnius University, Lithuania
In the theoretical hydromechanics special attention is given to the investigation of problems in unbounded domains, in particular, in domains with semi-infinite outlets to infinity. The boundary value problems in domains with cylindrical outlets (pipes) belong to this class. This is...
Recent results on regularity for the Navier-Stokes equations
2000-01-28
Speaker: Namkwon Kim, CMAF, Universidade de Lisboa, Portugal and University of Seoul, Korea
Local in time smooth solutions for the Navier-Stokes equations have not been known to persist for a long time. There have been several conditions which assure the persistence, for example, Serrin's conditions, etc... In this talk, we deal with some of the variants of Serrin's conditions and...
Free boundary problems for parabolic equations
2000-01-14
Speaker: Galina Bizhanova, Almaty State University, Kazakhistan
Many-dimensional free boundary problems for second order parabolic equations are considered. Two questions are studied: transformation of the unknown boundaries into prescribed ones and existence and uniqueness of the solutions to the problems in Hölder spaces and coercive estimates for...
Resultados de extrapolação em espaços de funções
1999-12-17
Speaker: Júlio Neves, Universidade de Coimbra, Portugal and University of Sussex, UK
Area(s): ...
Resultados de extrapolação em espaços de funções
1999-12-17
Speaker: Júlio Neves, Universidade de Coimbra, Portugal
Area(s): ...
Polinómios q-clássicos: um estudo unificado
1999-12-10
Speaker: Renato Alvarez-Nodarse, Universidade de Sevilha, Spain
O objectivo do seminário é estabelecer várias caracterizações dos chamados polinómios ortogonais q-clássicos (segundo Hahn), identificando as distintas famílias q-clássicas com certas famílias que figuram nos famosos esquemas de Askey e de Nikiforov et al.; em particular, apresentam-se duas...
Identificação de obstáculos através da difracção de ondas acústicas
1999-12-03
Speaker: Carlos Alves, Instituto Superior Técnico, Portugal
A detecção de obstáculos a partir do conhecimento do campo incidente e do campo difractado é um problema inverso com diversas aplicações ao nível da imagiologia. Do ponto de vista matemático trata-se de um problema não-linear e mal-posto. Resultados recentes permitiram estabelecer unicidade...
A uniqueness result for a degenerate parabolic problem
1999-11-19
Speaker: Noureddine Igbida, CMAF, Universidade de Lisboa, Portugal
We prove uniqueness of a weak solution for a degenerate parabolic problem arising in various physical models. The technique is based in showing that every weak solution is also an entropy solution in the sense of Carrillo and then in adapting the known techniques that give the uniqueness for...
Aproximação por funções de suporte compacto em domínios irregulares
1999-11-05
Speaker: António Caetano, Universidade de Aveiro, Portugal
Comparam-se os espaços gerais de Besov e de Triebel-Lizorkin sobre domínios com fronteira irregular com o completamento, naqueles espaços, do subconjunto das funções infinitamente continuamente diferenciáveis com suporte compacto nos mesmos domínios. Verifica-se que o conjunto dos parâmetros...
Quasilinear hyperbolic systems and dissipative mechanisms
1999-10-22
Speaker: Hsiao Ling, Academia Sinica, China
The talk is given to introduce recent developments on the subject of quasilinear hyperbolic systems with dissipation,particularly the systems of hyperpolic conservation laws with either lower order dissipation such as frictional damping and relaxation, or higher order dissipation such as...
A never failing polynomial solver
1999-06-24
Speaker: Stephan Ruscheweyh, Mathematisches Institut, Universitaet Wuerzburg, Germany
Area(s): ...
Linearization and connection problems for orthogonal polynomials
1999-06-08
Speaker: Renato Alvarez-Nodarse, Dept. of Mathematical Analysis, Univ. of Seville, Spain
Area(s): ...
Non-linear system of hyperbolic PDE and problems of equilibrium for logarithmic potential
1999-06-02
Speaker: Alexander Aptekarev, Lomonosov University, Moscow, Russia
Area(s): ...
Problemas com papel quadriculado
1999-05-19
Speaker: Valery Vavilov, Lomonosov University, Moscow, Russia
Area(s): ...
A never failing polynomial solver
Speaker: Stephan Ruscheweyh, Mathematisches Institut, Universitaet Wuerzburg, Germany
Area(s): ...
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