A cross-diffusion system obtained via (convex) relaxation in the JKO scheme

par Romain Ducasse (Université de Paris (LJLL))

lundi 9 mai 2022, 11:00 → 12:00 Europe/Paris

1013 (Université Paris-Cité - Bâtiment Sophie Germain)

In this talk, we will start from a very natural system of cross-diffusion equations, which can be seen as the gradient flow for the  Wasserstein distance of a certain functional. Unfortunately, this cross-diffusion system is not well-posed (this is a consequence of the fact that the underlying functional is not lower semi-continuous). We then consider the relaxation of the functional, and we prove existence of a solution in a suitable sense for the gradient flow (of the relaxed functional). This gradient flow has also a cross-diffusion structure, but the mixture between two different regimes, that are determined by the relaxation, makes this study non-trivial.

This work is a collaboration with F. Santambrogio and H. Yoldas