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

Mostafa Bendahmane; Mostafa Bendahmane

doi:10.3934/nhm.2008.3.863

Networks and Heterogeneous Media

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: 01 September 2007 Revised: 01 January 2008
Primary: 35K57, 35K55, 92B05

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].
- reaction-diffusion system,
- predator-prey,
- prey-taxis,
- Schauder fixed-point,
- weak solution,
- existence,
- uniqueness
Citation: Mostafa Bendahmane. Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis[J]. Networks and Heterogeneous Media, 2008, 3(4): 863-879. doi: 10.3934/nhm.2008.3.863

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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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