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

Zhi-Xian Yu, Rong Yuan

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

Keywords


Traveling wave solutions; convolution; cross-iteration; Schauder's fixed point theorem



DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2321



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.