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December  2006, 5(4): 733-762. doi: 10.3934/cpaa.2006.5.733

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, Norway

Received  September 2004 Revised  February 2005 Published  September 2006

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.
Keywords: uniqueness., anisotropic diffusion, existence, Reaction-diffusion-advection system, integrable data, renormalized solution.
Mathematics Subject Classification: Primary: 35K57, 35K55, 92D3.
Citation: Mostafa Bendahmane, Kenneth H. Karlsen. Renormalized solutions of an anisotropic reaction-diffusion-advection system with $L^1$ data. Communications on Pure & Applied Analysis, 2006, 5 (4) : 733-762. doi: 10.3934/cpaa.2006.5.733
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