Mathematical and numerical analysis for Predator-prey system in a polluted environment
Verónica Anaya - 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.
Received: January 2010; Revised: April 2010; Published: November 2010.
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