Networks and Heterogeneous Media (NHM)

Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis

Pages: 863 - 879, Volume 3, Issue 4, December 2008      doi:10.3934/nhm.2008.3.863

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Mostafa Bendahmane - Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile (email)

Abstract: In this paper, 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. This paper is a generalization of the results obtained in [2].

Keywords:  reaction-diffusion system, predator-prey, prey-taxis, Schauder fixed-point, weak solution, existence, uniqueness
Mathematics Subject Classification:  Primary: 35K57, 35K55, 92B05

Received: September 2007;      Revised: January 2008;      Available Online: October 2008.