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

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  • 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.
    Mathematics Subject Classification: Primary: 35K57, 35M10; Secondary: 35A05.


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