Traveling wave solutions for delayed reaction-diffusion systems
Analysis of PDEs
2010-07-21 v1
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.
Cite
@article{arxiv.1007.3429,
title = {Traveling wave solutions for delayed reaction-diffusion systems},
author = {Canrong Tian and Zhigui Lin},
journal= {arXiv preprint arXiv:1007.3429},
year = {2010}
}