Traveling wave solutions for delayed reaction-diffusion systems

Details Traveling wave solutions for delayed reaction-diffusion systems Traveling wave solutions for delayed reaction-diffusion systems

2010-07-20

arxiv.org/abs/1007.3429v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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