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Pre-Publicación 2013-22

Veronica Anaya, Mostafa Bendahmane, Michael Langlais, Mauricio Sepúlveda:

A convergent finite volume method for a model of indirectly transmitted diseases with nonlocal cross-diffusion

Abstract:

In this paper, we are concerned with a finite volume method for a model with cross-diffusion of the indirect transmission of an epidemic disease between two spatially distributed host populations having non-coincident spatial domains, transmission occurring through a contaminated environment. The mobility of each class is assumed to be influenced by the gradient of the other classes. We propose a Finite Volume scheme and proved the well-posedness, nonnegativity and convergence of the discrete solution. The convergence proof is based on deriving a series of a priori estimates and by using a general Lp compactness criterion. Additionally, we address the questions of existence of weak solutions and existence and uniqueness of classical solution by using, respectively, a regularization method and an interpolation result between Banach spaces. The proofs of these results are given in the Appendix. Finally, the numerical scheme is illustrated by some examples.

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Esta prepublicacion dio origen a la(s) siguiente(s) publicación(es) definitiva(s):

Veronica ANAYA, Mostafa BENDAHMANE, Michael LANGLAIS, Mauricio SEPúLVEDA: A convergent finite volume method for a model of indirectly transmitted diseases with nonlocal cross-diffusion. Computers & Mathematics with Applications, vol. 70, 2, pp. 132-157, (2015).