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Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis. (English) Zbl 1160.35438

Summary: We consider a system of nonlinear partial differential equations modeling the Lotka Volterra interactions of preys and actively moving predators with prey-taxis and spatial diffusion. The interaction between predators are modelized by the statement of a food pyramid condition. We establish the existence of weak solutions by using Schauder fixed-point theorem and uniqueness via duality technique.

MSC:

35K57 Reaction-diffusion equations
35K55 Nonlinear parabolic equations
92B05 General biology and biomathematics
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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