A finite-volume scheme for a cross-diffusion model arising from interacting many-particle population systems

TL;DR

This paper develops a finite-volume numerical scheme for a cross-diffusion model derived from many-particle population interactions, proving solution existence and entropy properties.

Contribution

It introduces a novel finite-volume scheme for a complex cross-diffusion system with proven discrete entropy inequalities.

Findings

Existence of discrete solutions established

Discrete entropy production inequality proved

Scheme applicable to multi-species population models

Abstract

A finite-volume scheme for a cross-diffusion model arising from the mean-field limit of an interacting particle system for multiple population species is studied. The existence of discrete solutions and a discrete entropy production inequality is proved. The proof is based on a weighted quadratic entropy that is not the sum of the entropies of the population species.