On triangular reaction cross-diffusion systems with possible self-diffusion

TL;DR

This paper establishes the existence of global solutions for a class of reaction cross-diffusion systems with potential self-diffusion, using entropy and duality methods, extending results for the triangular SKT system in population dynamics.

Contribution

It introduces new existence results for reaction cross-diffusion systems with self-diffusion, extending the analysis of the triangular SKT system.

Findings

Proved global existence of solutions for a broad class of reaction cross-diffusion systems.

Extended the analysis of the triangular SKT system to include self-diffusion terms.

Utilized entropy and duality methods to establish key results.

Abstract

We present new results of existence of global solutions for a class of reaction cross-diffusion systems of two equations presenting a cross-diffusion term in the first equation, and possibly presenting a self-diffusion term in any (or both) of the two equations. This class of systems arises in Population Dynamics, and notably includes the triangular SKT system. In particular, we recover and extend existing results for the triangular SKT system. Our proof relies on entropy and duality methods.