Renormalized solutions of an anisotropic reaction-diffusion-advection system with $L^1$ data

Mostafa Bendahmane; Kenneth H. Karlsen

doi:10.3934/cpaa.2006.5.733

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2006, Volume 5, Issue 4: 733-762. Doi: 10.3934/cpaa.2006.5.733

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Renormalized solutions of an anisotropic reaction-diffusion-advection system with $L^1$ data

Mostafa Bendahmane^1, and
Kenneth H. Karlsen^1,

1.
Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo

Received: August 31, 2004

Revised: January 31, 2005

Published: November 2006

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Abstract

We prove existence of a renormalized solution to a system of nonlinear partial differential equations with anisotropic diffusivities and transport effects, supplemented with initial and Dirichlet boundary conditions. The data are assumed to be merely integrable. This system models the spread of an epidemic disease through a heterogeneous habitat.

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Mathematics Subject Classification: Primary: 35K57, 35K55, 92D30.

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