Global existence of solutions for some coupled systems of reaction-diffusion equations

TL;DR

This paper proves the global existence of classical solutions for certain coupled reaction-diffusion systems modeling infectious disease spread, focusing on systems with triangular matrix diffusion and weakly exponential growth nonlinearities.

Contribution

It introduces a new proof of global existence for coupled reaction-diffusion systems with triangular matrix diffusion and weakly exponential nonlinearities.

Findings

Global existence of classical solutions established

Applicable to systems with weakly exponential growth nonlinearities

Utilizes triangular matrix diffusion structure

Abstract

The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a triangular matrix diffusion and we show that we can prove global existence of classical solutions for the nonlinearities of weakly exponential growth.