Forced waves in a Lotka-Volterra competition-diffusion model with a shifting habitat

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:276

Article

Dong, Fang-Di^1,2  Li, Bingtuan²  Li, Wan-Tong¹ 

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China

[2] Univ Louisville, Dept Math, Louisville, KY 40292 USA

关键词: Reaction-diffusion equation;    Shifting habitat;    Competition;    Linear determinacy;    Forced traveling waves;   

DOI  :  10.1016/j.jde.2020.12.022

来源: Elsevier

【 摘 要 】

We establish the existence of traveling waves for a Lotka-Volterra competition-diffusion model with a shifting habitat. It is assumed that the growth rate of each species is nondecreasing along the x-axis, positive near infinity and negative near -infinity, and shifting rightward at a speed c. We show that under appropriate conditions, for the case that one species is competitively stronger near infinity and the case that both species coexist near infinity, there exists a critical number (c) over bar(infinity) such that for any c > (c) over bar(infinity) there exists a forced traveling wave with speed c connecting the origin and a semi-trivial steady state and for c < <(c)over bar>(infinity) such a traveling wave does not exist. We also show that when a coexistence steady state exists, for any c > 0, there is a forced traveling wave with speed c connecting the origin and the coexistence steady state. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free