A cross-diffusion system obtained via (convex) relaxation in the JKO scheme - INSA Lyon - Institut National des Sciences Appliquées de Lyon
Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2022

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

Résumé

In this paper, we start from a very natural system of cross-diffusion equations which, unfortunately, is not well-posed as it is the gradient flow for the Wasserstein distance of a functional which is not lower semi-continuous due to lack of convexity of the integral. We then compute the convexification of the integral and prove existence of a solution in a suitable sense for the gradient flow of the corresponding relaxed functional. This gradient flow has also a cross-diffusion structure but the mixture between two different regimes which are determined by the convexification makes this study non-trivial.
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hal-03719155 , version 1 (10-01-2025)

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Romain Ducasse, Filippo Santambrogio, Havva Yoldaş. A cross-diffusion system obtained via (convex) relaxation in the JKO scheme. Calculus of Variations and Partial Differential Equations, 2022, 62 (1), pp.29. ⟨10.1007/s00526-022-02356-8⟩. ⟨hal-03719155⟩
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