Study of a class of triangular starvation driven cross-diffusion systems

TL;DR

This paper investigates the mathematical properties such as existence, regularity, and uniqueness of solutions for a broad class of triangular reaction-cross-diffusion systems modeling competitive species influenced by starvation.

Contribution

It introduces a new analytical framework for these systems and proves existence results using Schauder's fixed point theorem, advancing understanding of their mathematical behavior.

Findings

Existence of solutions established for the class of systems

Regularity and uniqueness results obtained

Application to models of starvation-driven species competition

Abstract

We study the existence, regularity and uniqueness for a general class of triangular reaction-cross-diffusion systems coming from the study of starvation driven behavior for two species in competition. This study involves an equivalent system in non-divergence form, for which existence can be obtained thanks to Schauder's fixed point theorem.