Traveling wave solutions in nonlocal reaction-diffusion systems with delays and applications

Abstract

This paper deals with two-species convolution diffusion-competition models of the Lotka--Volterra type with delays which describe more accurate information than the Laplacian diffusion-competition models. We first investigate the existence of travelling wave solutions of a class of nonlocal convolution diffusion systems with weak quasimonotonicity or weak exponential quasimonotonicity by a cross-iteration technique and Schauder's fixed point theorem. When the results are applied to the convolution diffusion-competition models with delays, we establish the existence of traveling wave solutions as well as asymptotic behavior. doi:10.1017/S1446181109000406