A Free Boundary Problem for the Predator-Prey Model with Double Free Boundaries

摘要

In this paper we investigate a free boundary problem for the classical Lotka-Volterra type predator-prey 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 and are described by Stefan-like condition. We prove a spreading-vanishing dichotomy for this model, namely the predator species either successfully spreads to infinity as at both fronts and survives in the new environment, or it spreads within a bounded area and dies out in the long run while the prey species stabilizes at a positive equilibrium state. The long time behavior of solution and criteria for spreading and vanishing are also obtained.