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

Mostafa Bendahmane

doi:10.3934/nhm.2008.3.863

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2008, Volume 3, Issue 4: 863-879. Doi: 10.3934/nhm.2008.3.863

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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

Received: August 31, 2007

Revised: December 31, 2007

Published: November 2008

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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].

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Mathematics Subject Classification: Primary: 35K57, 35K55, 92B05.

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