On some free boundary problems of the prey-predator model
On some free boundary problems of the prey-predator model
复制标题
关于捕食者模型的一些自由边界问题
DOI：
10.1016/j.jde.2014.02.013
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发表时间：
2014
影响因子：
2.4
通讯作者：
王明新
中科院分区：
文献类型：
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作者：
王明新
本文研究了一维Lotka-Volterra型食饵-捕食模型的自由边界问题。主要目的是了解两个物种（猎物和捕食者）通过自由边界传播的渐近行为。我们证明了一个传播-消失的二分法，即这两个物种要么随着时间的推移而成功传播到整个空间并在新的环境中生存，要么从长远来看它们无法建立并消亡。得到了解的长时间性态和扩散与消失的判据。最后，当传播成功时，我们提供了一个估计，表明传播速度（如果存在）不能快于移动波前解的最小速度的食饵-捕食模型在整个真实的线上没有自由边界。
In this paper we investigate some free boundary problems for the Lotka–Volterra type prey–predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading via a free boundary. We prove a spreading–vanishing dichotomy, namely the two species either successfully spread to the entire space as timetgoes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of solution and criteria for spreading and vanishing are also obtained. Finally, when spreading successfully, we provide an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the prey–predator model on the whole real line without a free boundary.