New results for triangular reaction cross diffusion system

TL;DR

This paper introduces an entropy and duality-based approach to analyze a class of triangular reaction cross diffusion systems, extending existing results on the classical model.

Contribution

It develops a novel analytical method that broadens the understanding of triangular reaction cross diffusion systems, especially the classical Shigesada-Kawasaki-Teramoto model.

Findings

Extended classical results on the triangular SKT model.

Developed a new entropy and duality framework.

Provided new insights into the behavior of cross diffusion systems.

Abstract

We present an approach based on entropy and duality methods for triangular reaction cross diffusion systems of two equations, in which cross diffusion terms appear only in one of the equations. Thanks to this approach, we recover and extend many existing results on the classical triangular Shigesada-Kawasaki-Teramoto model.