## Preprint 2009-23

## Veronica Anaya, Mostafa Bendahmane, Mauricio Sepúlveda:

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

### 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, and shown that the scheme converges to the corresponding weak solution for the studied model. 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.

This preprint gave rise to the following definitive publication(s):

**Veronica ANAYA, Mostafa BENDAHMANE, Mauricio SEPúLVEDA: ***Mathematical and numerical analysis for predator-prey system in a polluted environment*. Networks and Heterogeneous Media, vol. 5, 4, pp. 813-847, (2010)