Biological invasion in a predator–prey model with a free boundary

In this paper we study a predator-prey system with free boundary in a one-dimensional environment. The predator v is the invader which exists initially in a sub-interval [0, s 0 ] of [0, L] and has the Leslie-Gower terms that measure the loss in the predator population due to rarity of the prey. The prey u (the native species) is initially distributed over the whole region [0, L]. Our primary goal is to understand how the success or failure of the predator's invasion is affected by the initial datum v 0 . We derive a spreading-vanishing dichotomy and give sharp criteria for spreading and vanishing in this model.

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