Room FC1 007, DMat UPorto
11h00 - Maria Elisa Barbosa Silveira
Drug release enhanced by temperature: an accurate discrete model for solutions in H^3.
Abstract: In this talk we consider the coupling between two quasilinear diffusion equations: the diffusion coefficient of the first equation depends on its solution and the diffusion and convective coefficient of the second equation depend on the solution of the first one. This system can be used to describe the drug evolution in a target tissue when the drug transport is enhanced by heat. We study, from an analytical and a numerical viewpoints, the coupling of the heat equation with the drug diffusion equation. A fully discrete piecewise linear finite method is proposed for this system and we establish its stability. Assuming that the heat and the concentration are in H^3 we prove that the introduced method is second order convergent. Numerical experiments illustrating the theoretical results are also included.
11h30 - Nuno Picado
Deciding about the emptiness of the interior of a manifold based on a sample of points
Abstract: In this talk, I will present some results about a method to decide, based on a sample of points from a manifold M, whether its interior is empty or not. This method was introduced in the article "Stochastic detection of some topological and geometric feature" by Cuevas et al. for independent random variables and sufficiently smooth manifolds. The decision process is based on an estimator constructed using balls centered at the points of the sample. We will show that the approach still holds if the sample satisfies a suitable dependence assumption. After this, the talk will be focused on the construction of models with the type of dependence needed for the results.
12h00 - Dieudonné Mbouna
(M,N)-Coherent pairs of order (m,k) and Sobolev Orthogonal Polynomials on the non-uniform lattice
ABOUT THE SPEAKERS:
Maria Elisa B. Silveira is a PhD student of the Joint PhD Program UC|UP, working at the University of Coimbra, in Numerical Analysis, under the supervision of Professor José Augusto Ferreira.
Nuno Picado is a PhD student of the Joint PhD Program UC|UP, working at the University of Coimbra, in Probability and Statistics, under the supervision of Professor Paulo Eduardo Oliveira.
Dieudonné Mbouna is a PhD student of the Joint PhD Program UC|UP, working at the University of Coimbra, in Analysis, under the supervision of Professor José Carlos Petronilho.