A nonlocal diffusion model with free boundaries in spatial heterogeneous environment

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Cao, Jia-Feng¹  Li, Wan-Tong¹  Zhao, Meng¹ 

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

关键词: Nonlocal diffusion;    Free boundary;    Spatial heterogeneity;    Sign indefinite;    Spreading-vanishing dichotomy;    Spreading speed;   

DOI  :  10.1016/j.jmaa.2016.12.044

来源: Elsevier

【 摘 要 】

This paper is concerned with the nonlocal diffusive model with double free boundaries in spatial heterogeneous environment, where the spatial heterogeneity is described by the sign indefinite coefficients. Such a model can be used to illustrate the spreading or vanishing of a. new or invasive species. Due to the lack of comparison principle in the nonlocal reaction diffusion equation, many classical methods cannot be used directly to this nonlocal problem. This motivates us to find new techniques. We first establish the spreading vanishing dichotomy as well as some criteria that ensure the species spreading or vanishing by principal eigenvalues of associated scalar elliptic eigenvalue problems. And then we determine the spreading speed when spreading occurs. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free