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ABOUT THE ENTROPIC STRUCTURE OF DETAILED BALANCED MULTI-SPECIES CROSS-DIFFUSION EQUATIONS

Abstract : This paper links at the formal level the entropy structure of a multi-species cross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type satisfying the detailed balance condition with the entropy structure of a reversible microscopic many-particle Markov process on a discretised space. The link is established by first performing a mean-field limit to a master equation over discretised space. Then the spatial discretisation limit is performed in a completely rigorous way. This by itself provides a novel strategy for proving global existence of weak solutions to a class of cross-diffusion systems.
Keywords : Analysis of PDEs
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Submitted on : Monday, February 11, 2019 - 4:39:45 PM
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Esther Daus, Laurent Desvillettes, Helge Dietert. ABOUT THE ENTROPIC STRUCTURE OF DETAILED BALANCED MULTI-SPECIES CROSS-DIFFUSION EQUATIONS. Journal of Differential Equations, Elsevier, 2019, 266 (7), pp.3861-3882. ⟨10.1016/j.jde.2018.09.020⟩. ⟨hal-02014656⟩

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