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December  2008, 3(4): 863-879. doi: 10.3934/nhm.2008.3.863

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

Mostafa Bendahmane 1,

1. 

Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Received  September 2007 Revised  January 2008 Published  October 2008

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: weak solution, reaction-diffusion system, Schauder fixed-point, uniqueness, prey-taxis, predator-prey, existence.
Mathematics Subject Classification: Primary: 35K57, 35K55, 92B05.
Citation: Mostafa Bendahmane. Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis. Networks & Heterogeneous Media, 2008, 3 (4) : 863-879. doi: 10.3934/nhm.2008.3.863
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