Global Existence for some Cross Diffusion Systems with Equal Cross Diffusion/Reaction Rates

TL;DR

This paper proves the global existence of strong solutions for certain cross diffusion systems inspired by biological models, specifically when these systems have equal diffusion or reaction rates across multiple species, on bounded domains of any dimension.

Contribution

It establishes the first global existence results for these specific cross diffusion systems with equal rates, extending previous work to arbitrary dimensions.

Findings

Global existence of strong solutions proven

Applicable to systems with equal diffusion or reaction rates

Valid on bounded domains of any dimension

Abstract

We consider some cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in population biology. We establish the global existence of strong solutions to systems for multiple species having equal either diffusion or reaction rates. The systems are given on bounded domains of arbitrary dimension.