期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 38, 期 5, 页码 2591-2607出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2018109
关键词
Leslie-Gower model; free boundary problem; spreading-vanishing dichotomy; long time behavior; criteria for spreading and vanishing
资金
- NSFC [11771110, 11371113]
In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the free boundaries represent expanding fronts of the predator species. We first prove the existence, uniqueness and regularity of global solution. Then provide a spreading-vanishing dichotomy, namely the predator species either successfully spreads to infinity as t -> infinity at both fronts and survives in the new environment, or it spreads within a bounded area and dies out in the long run. The long time behavior of (u,v) and criteria for spreading and vanishing are also obtained. Because the term v/u (which appears in the second equation) may be unbounded when u nears zero, it will bring some difficulties for our study.
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