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

Pages: 813 - 847, Volume 5, Issue 4, December 2010

doi:10.3934/nhm.2010.5.813       Abstract        References        Full Text (7625.0K)       Related Articles

Verónica Anaya - Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile (email)
Mostafa Bendahmane - Institut de Mathématiques de Bordeaux, Université Victor Segalen Bordeaux 2, 33076 Bordeaux, France (email)
Mauricio Sepúlveda - CI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile (email)

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.

Keywords:  Predator-prey system, weak solution, existence, Finite volume - Finite element scheme.
Mathematics Subject Classification:  Primary: 35K57, 35M10; Secondary: 35A05.

Received: January 2010;      Revised: April 2010;      Published: November 2010.

 References