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

Part of: Miscellaneous topics - Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  09 March 2010

ZHI-XIAN YU  and
RONG YUAN
ZHI-XIAN YU*
Affiliation:
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)
RONG YUAN
Affiliation:
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)
*
✉For correspondence; e-mail: yuzx@mail.bnu.edu.cn
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Abstract

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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.

Keywords

travelling wave solutionsconvolutioncross-iterationSchauder’s fixed point theorem

MSC classification

Secondary: 35K57: Reaction-diffusion equations 35R10: Partial functional-differential equations
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 1 , July 2009 , pp. 49 - 66
Copyright
Copyright © Australian Mathematical Society 2010

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