The ANZIAM Journal

Cambridge Journals Online - CUP Full-Text Page
The ANZIAM Journal (2009), 51:49-66 Cambridge University Press
Copyright © Australian Mathematical Society 2010
doi:10.1017/S1446181109000406

Research Article

TRAVELLING WAVE SOLUTIONS IN NONLOCAL REACTION–DIFFUSION SYSTEMS WITH DELAYS AND APPLICATIONS


ZHI-XIAN YUa1 c1 and RONG YUANa1

a1 School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China (email: yuzx@mail.bnu.edu.cn, ryuan@bnu.edu.cn)
Article author query
yu zx [Google Scholar]
yuan r [Google Scholar]

Abstract

This paper deals with two-species convolution diffusion-competition models of 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 travelling wave solutions as well as asymptotic behaviour.

(Received April 17 2009)

(Revised August 14 2009)

2000 Mathematics subject classificationprimary 35K57; secondary 92D25; 35R10

Keywords and phrasestravelling wave solutions; convolution; cross-iteration; Schauder’s fixed point theorem

Correspondence:

c1 For correspondence; e-mail: yuzx@mail.bnu.edu.cn