Publication Date:
2019
Description:
〈p〉Publication date: 15 March 2019〈/p〉
〈p〉〈b〉Source:〈/b〉 Journal of Differential Equations, Volume 266, Issue 7〈/p〉
〈p〉Author(s): Esther S. Daus, Laurent Desvillettes, Helge Dietert〈/p〉
〈h5〉Abstract〈/h5〉
〈div〉〈p〉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.〈/p〉〈/div〉
Print ISSN:
0022-0396
Electronic ISSN:
1090-2732
Topics:
Mathematics
