Travelling wave solutions in non-local convolution diffusive competitive-cooperative systems

In this paper, we investigate the existence of travelling wave solutions for the non-local convolution diffusion two-species competitive-cooperative systems by using Schauder's fixed-point theorem and a cross-iteration technique. If the non-local diffusion kernel where δ is the Dirac delta func...

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Bibliographic Details
Published in:IMA journal of applied mathematics 2011-08, Vol.76 (4), p.493-513
Main Authors: Yu, Zhi-Xian, Yuan, Rong
Format: Article
Language:English
Subjects:
Convolution
Delta function
Diffusion
Exact sciences and technology
Existence theorems
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Sciences and techniques of general use
Theorems
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Traveling waves
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Summary:In this paper, we investigate the existence of travelling wave solutions for the non-local convolution diffusion two-species competitive-cooperative systems by using Schauder's fixed-point theorem and a cross-iteration technique. If the non-local diffusion kernel where δ is the Dirac delta function, then we can obtain the results in Huang & Zou (2006, Travelling wave solutions in delayed reaction diffusion systems with partial monotonicity. Acta Math. Appl. Sinica, 22, 243-256) and the existence of travelling waves for the corresponding Laplacian diffusion two-species competitive-cooperative systems.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxq048