Publisher： Cambridge University Press
E-ISSN： 1446-8735|51|1|49-66
ISSN： 1446-1811
Source： ANZIAM Journal, Vol.51, Iss.1, 2009-07, pp. : 49-66
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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.
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