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.

arXiv comment20 pages (small corrections)

References in corpus (3)

• Global existence analysis of cross-diffusion population systems for multiple species
• Cross-diffusion systems and fast-reaction limits
• Convergence of a Finite-Volume Scheme for a Degenerate Cross-Diffusion Model for Ion Transport

Cited by in corpus (4)

• Rigorous mean-field limit and cross diffusion
• Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems
• Persisting entropy structure for nonlocal cross-diffusion systems
• Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit