Invasion traveling wave solutions of a competitive system with dispersal

Boundary value problems

Shuxia Pan¹  Guo Lin³ 

[1] Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, People’School of Mathematics and Statistics, Lanzhou University, Lanzhou, People’s Republic of China

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

DOI  :  10.1186/1687-2770-2012-120

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY