A reaction-diffusion system with cross-diffusion modelling the spread of an epidemic disease Article - 2010

Mostafa Bendahmane, Michel Langlais

Mostafa Bendahmane, Michel Langlais, « A reaction-diffusion system with cross-diffusion modelling the spread of an epidemic disease  », Journal of Evolution Equations, 2010, pp. 883-904. ISSN 1424-3199

Abstract

We provide existence results for nonnegative solutions to a class of reaction-diffusion systems with cross-diffusion modeling the spread of an epidemic disease. The existence of weak solutions is proved by means of an approximation process, the Faedo-Galerkin method, and a compactness argument. Under additional assumptions a global existence result for classical solutions is derived upon using interpolation results between Banach spaces.

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