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In this paper we investigate a free boundary problem for a predator-preymodel with double free boundaries in one space dimension. This system modelsthe expanding of an invasive or new predator species in which the freeboundaries represent expanding fronts of the predator species and are describedby Stefan-like condition. We prove a spreading-vanishing dichotomy for thismodel, namely the predator species either successfully spreads to infinity as$t\to \infty$ at both fronts and survives in the new environment, or it failsto establish and dies out in the long run while the prey species stabilizes ata positive equilibrium state. The long time behavior of solution and criteriafor spreading and vanishing are also obtained.

A Free Boundary Problem for a Predator-prey Model with Double Free Boundaries