Spreading and vanishing in a diffusive prey-predator model with variable intrinsic growth rate and free boundary

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:441

Article

Wang, Mingxin¹  Sheng, Weijie¹  Zhang, Yang² 

[1] Harbin Inst Technol, Nat Sci Res Ctr, Harbin 150080, Peoples R China

[2] Harbin Engn Univ, Dept Math, Harbin 150001, Peoples R China

关键词: Diffusive prey-predator model;    Variable intrinsic growth rate;    Free boundary;    Spreading and vanishing;    Long time behavior;   

DOI  :  10.1016/j.jmaa.2016.04.007

来源: Elsevier

【 摘 要 】

We study the spreading and vanishing phenomena in a diffusive prey predator system with variable intrinsic growth rate and free boundary. In this model, the free boundary represents the spreading front and is caused only by the prey, and the variable intrinsic growth rate is allowed to tend to zero and decay very fast as t -> infinity or x -> infinity. Our main attention is on the effect of variable intrinsic growth rate on the solution and attempt to find some new techniques to deal with the variable intrinsic growth rate. We first study the long time behavior of (u, v) for the vanishing case (h(infinity) < infinity). Then we find the criteria for spreading and vanishing. At last, the long time behavior of (u, v) for the spreading case (h(infinity) = infinity) is discussed. Theorems 2.2, 2.3 and 4.1 together establish a spreading vanishing dichotomy. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free