On a free boundary problem for a reaction-diffusion-advection logistic model in heterogeneous environment

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Monobe, Harunori¹  Wu, Chang-Hong² 

[1] Tokyo Inst Technol, Sch Sci, Meguro Ku, 2-12-1 Ookayama, Tokyo 1528551, Japan

[2] Natl Univ Tainan, Dept Appl Math, Tainan 700, Taiwan

关键词: Free boundary problem;    Reaction-diffusion-advection equation;    Heterogeneous environments;    Population dynamics;   

DOI  :  10.1016/j.jde.2016.08.033

来源: Elsevier

【 摘 要 】

In this paper, we investigate a reaction-diffusion-advection equation with a free boundary which models the spreading of an invasive species in one-dimensional heterogeneous environments. We assume that the species has a tendency to move upward along the resource gradient in addition to random dispersal, and the spreading mechanism of species is determined by a Stefan-type condition. Investigating the sign of the principal eigenvalue of the associated linearized eigenvalue problem, under certain conditions we obtain the sharp criteria for spreading and vanishing via system parameters. Also, we establish the long-time behavior of the solution and the asymptotic spreading speed. Finally, some biological implications are discussed. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free