About the entropic structure of detailed balanced multi-species cross-diffusion equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Daus, Esther S.¹  Desvillettes, Laurent²  Dietert, Helge² 

[1] Vienna Univ Technol, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

[2] Univ Paris Diderot, CNRS, IMJ PRG, F-75013 Paris, France

关键词: Population dynamics;    Shigesada-Kawasaki-Teramoto system;    Mean-field limit;    Detailed balance;    Entropy method;    Onsager's principle;   

DOI  :  10.1016/j.jde.2018.09.020

来源: Elsevier

【 摘 要 】

This paper links at the formal level the entropy structure of a multi-species cross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type (cf. [1]) 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free