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This paper concerns with existence, uniqueness and asymptotic behavior of thesolutions for a nonlocal coupled system of reaction-diffusion. We prove theexistence and uniqueness of weak solutions by the Faedo-Galerkin method andexponential decay of solutions by the classic energy method. We improve theresults obtained by Chipot-Lovato and Menezes for coupled systems. A numericalscheme is presented.

Solution and Asymptotic Behavior for a Nonlocal Coupled System of Reaction-Diffusion