Predator-prey model with a free boundary

In this paper, we consider a Leslie-Gower predator-prey model in one-dimensional environment. First, we investigate the mathematical questions of the problem. A priori estimates of Schauder type, which are necessary for the solvability of the problem are established. The predator v is the invader which exists initially in a sub-interval [0, s0] 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]. Uniqueness of the solution is shown and qualitative properties of the solution are investigated.

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