Open Access Research

Invasion traveling wave solutions of a competitive system with dispersal

Shuxia Pan1* and Guo Lin2

Author Affiliations

1 Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People’s Republic of China

2 School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People’s Republic of China

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Boundary Value Problems 2012, 2012:120  doi:10.1186/1687-2770-2012-120

Published: 24 October 2012

Abstract

This paper is concerned with the invasion traveling wave solutions of a Lotka-Volterra type competition system with nonlocal dispersal, the purpose of which is to formulate the dynamics between the resident and the invader. By constructing upper and lower solutions and passing to a limit function, the existence of traveling wave solutions is obtained if the wave speed is not less than a threshold. When the wave speed is smaller than the threshold, the nonexistence of invasion traveling wave solutions is proved by the theory of asymptotic spreading.

MSC: 35C07, 35K57, 37C65.

Keywords:
comparison principle; asymptotic spreading; upper and lower solutions; invasion waves