Systems with nonlocal vs. local diffusions and free boundaries

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Li, Lei¹  Sheng, Weijie¹  Wang, Mingxin^1,2 

[1] Harbin Inst Technol, Sch Math, Harbin 150001, Heilongjiang, Peoples R China

[2] Jiangxi Normal Univ, Coll Math & Informat Sci, Nanchang 330022, Jiangxi, Peoples R China

关键词: Nonlocal-local diffusions;    Free boundaries;    Existence-uniqueness;    Spreading-vanishing;    Long-time behavior;   

DOI  :  10.1016/j.jmaa.2019.123646

来源: Elsevier

【 摘 要 】

We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the population dispersal, with the free boundary representing the spreading front of the species. We first prove the existence, uniqueness and regularity of global solution. For the classical competition, prey-predator and mutualist models, we show that a spreading-vanishing dichotomy holds, and establish the criteria of spreading and vanishing, and long time behavior of the solution. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free