A weak competition system with advection and free boundaries

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:463

Article

Ren, Xinzhi¹  Liu, Lili^2,3  Liu, Xianning¹ 

[1] Southwest Univ, Minist Educ, Sch Math & Stat, Key Lab Ecoenvironm Gorges Reservoir Reg 3, Chongqing 400715, Peoples R China

[2] Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Shanxi, Peoples R China

[3] Shanxi Univ, Shanxi Key Lab Math Tech & Big Data Anal Dis Cont, Taiyuan 030006, Shanxi, Peoples R China

关键词: Reaction-diffusion-advection;    Free boundary;    Spreading speed;    Competition;    Minimal habitat size;   

DOI  :  10.1016/j.jmaa.2018.03.055

来源: Elsevier

【 摘 要 】

In order to study the influence of advection speed on the competitive outcomes of two invading species, a reaction-diffusion-advection weak competition system with four free boundaries in one dimensional space is proposed and investigated. In the case of small advection speed, the explicit classification of the competitive outcomes, the estimation of the spreading speed, the long time behavior of the solutions and the minimal habitat size which determines whether the species can always spread or not are obtained. The results are similar as the case with no advection. In the case of large advection speed, both two species cannot spread successfully, but may virtual spread downstream. In the case of medium-sized advection speed, some competitive outcomes and the long time behaviors of the solutions are also obtained. Mathematical results suggest that the competitive outcomes, which depend on the advection speed and moving parameters, are very complicated. Some criteria for spreading, vanishing and virtual spreading are also established in all cases. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free