【Analysis and Partial Differential Equations Seminar】A cross-diffusion system obtained via (convex) relaxation in the JKO scheme

Speaker: Prof. Yoldas Havva

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

Abstract: We start from a cross-diffusion system that is a gradient flow for the Wasserstein distance of a certain non-lower-semi continuous functional. We consider the relaxation of the functional and 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 the study non-trivial. This is a joint work (Calc. Var. PDE (2023) 62:23) with Romain Ducasse (Paris) and Filippo Santambrogio (Lyon).