Print Email Facebook Twitter A cross-diffusion system obtained via (convex) relaxation in the JKO scheme Title A cross-diffusion system obtained via (convex) relaxation in the JKO scheme Author Ducasse, Romain (Laboratoire Jacques-Louis Lions) Santambrogio, Filippo (Institut Camille Jordan; Institut Universitaire de France) Yoldas, H. (TU Delft Mathematical Physics) Date 2023 Abstract In this paper, we start from a very natural system of cross-diffusion equations, which can be seen as a gradient flow for the Wasserstein distance of a certain functional. Unfortunately, the cross-diffusion system is not well-posed, as a consequence of the fact that the underlying functional is not lower semi-continuous. We then 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 this study non-trivial. To reference this document use: http://resolver.tudelft.nl/uuid:998c1eaa-e220-47f0-b79e-bb74d4a9eebb DOI https://doi.org/10.1007/s00526-022-02356-8 ISSN 0944-2669 Source Calculus of Variations and Partial Differential Equations, 62 (1) Part of collection Institutional Repository Document type journal article Rights © 2023 Romain Ducasse, Filippo Santambrogio, H. Yoldas Files PDF s00526_022_02356_8.pdf 720.66 KB Close viewer /islandora/object/uuid:998c1eaa-e220-47f0-b79e-bb74d4a9eebb/datastream/OBJ/view