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

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.