Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Convex Sobolev inequalities related to unbalanced optimal transport
Publication Date:	2019-04-08
Authors:	- Stanislav Kondratyev - Dmitry Vorotnikov
Abstract:	We study the behaviour of various Lyapunov functionals (relative entropies) along the solutions of a family of nonlinear drift-diffusion-reaction equations coming from statistical mechanics and population dynamics. These equations can be viewed as gradient flows over the space of Radon measures equippedcwith the Hellinger-Kantorovich distance. The driving functionals of the gradient flows are not assumed to be geodesically convex or semi-convex. We prove new isoperimetric-type functional inequalities, allowing us to control the relative entropies by their productions, which yields the exponential decay of the relative entropies.
Institution:	DMUC 19-13
Online version:	http://www.mat.uc.pt...prints/eng_2019.html
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