Traveling wave solutions for delayed reaction-diffusion systems

TL;DR

This paper investigates the existence of traveling wave solutions in delayed reaction-diffusion systems with mixed quasimonotonicity, using monotone iteration and fixed point theorems, and provides practical criteria for their existence.

Contribution

It introduces a method to establish traveling wave solutions based on coupled upper and lower solutions for systems with mixed quasimonotonicity.

Findings

Existence of traveling wave solutions under certain conditions.

Reduction of the problem to constructing coupled quasi-upper and quasi-lower solutions.

Practical criteria for verifying the existence of traveling waves.

Abstract

This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iteration scheme and Schauder's fixed point theorem, it is shown that if the system has a pair of coupled upper and lower solutions, then there exists at least a traveling wave solution. More precisely, we reduce the existence of traveling waves to the existence of an admissible pair of coupled quasi-upper and quasi-lower solutions which are easy to construct in practice.