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

• Autores: Zhi-Xian Yu, Rong Yuan
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 51, Nº 1, 2009, págs. 49-66
• Idioma: inglés
• DOI: 10.1017/s1446181109000406
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• Resumen

  • 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.