A free boundary problem of a predator–prey model with higher dimension and heterogeneous environment

This paper is concerned with a free boundary problem for a prey–predator model in higher space dimensions and heterogeneous environment. Such a model may be used to describe the spreading of an invasive or new predator species in which the free boundary represents the spreading front of the predator species and is described by Stefan-like condition. For simplicity, we assume that the environment and solutions are radially symmetric. We prove a spreading–vanishing dichotomy for this model, namely the predator species either successfully spreads to infinity as t→∞t→∞ and survives in the new environment, or it fails to establish and dies out in the long run while the prey species stabilizes at a positive equilibrium state. The criteria for spreading and vanishing are given.