Mathematical and numerical analysis for Predator-prey system in a polluted environment

Verónica Anaya; Mostafa Bendahmane; Mauricio Sepúlveda; Verónica Anaya; Mostafa Bendahmane; Mauricio Sepúlveda

doi:10.3934/nhm.2010.5.813

Networks and Heterogeneous Media

2010, Volume 5, Issue 4: 813-847. doi: 10.3934/nhm.2010.5.813

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Mathematical and numerical analysis for Predator-prey system in a polluted environment

1.
Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción
2.
Institut de Mathématiques de Bordeaux, Université Victor Segalen Bordeaux 2, 33076 Bordeaux
3.
CI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción

Received: 01 January 2010 Revised: 01 April 2010
Primary: 35K57, 35M10; Secondary: 35A05.

In this paper, we prove existence results for a Predator-prey system in a polluted environment. The existence result is proved by the Schauder fixed-point theorem. Moreover, we construct a combined finite volume - finite element scheme to our model, we establish existence of discrete solutions to this scheme, and show that it converges to a weak solution. The convergence proof is based on deriving series of a priori estimates and using a general $L^p$ compactness criterion. Finally we give some numerical examples.
- Predator-prey system,
- weak solution,
- existence,
- Finite volume - Finite element scheme
Citation: Verónica Anaya, Mostafa Bendahmane, Mauricio Sepúlveda. Mathematical and numerical analysis for Predator-prey system in a polluted environment[J]. Networks and Heterogeneous Media, 2010, 5(4): 813-847. doi: 10.3934/nhm.2010.5.813

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Abstract

In this paper, we prove existence results for a Predator-prey system in a polluted environment. The existence result is proved by the Schauder fixed-point theorem. Moreover, we construct a combined finite volume - finite element scheme to our model, we establish existence of discrete solutions to this scheme, and show that it converges to a weak solution. The convergence proof is based on deriving series of a priori estimates and using a general $L^p$ compactness criterion. Finally we give some numerical examples.

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