Predator-prey model with a free boundary
A. N. ElmurodovV.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, University str., Tashkent 100174, UzbekistanIbodat KhaldibaevaTashkent State Technical University, Tashkent, UzbekistanNurila YuldoshevNational Research University "Tashkent Institute of Irrigation and Agricultural Mechanization Engineers", Tashkent, Uzbekistan
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Annotatsiya
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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