Preprint 2003-039

Renormalized Entropy Solutions for Quasilinear Anisotropic Degenerate Parabolic Equations.

Mostafa Bendahmane and Kenneth H. Karlsen

Abstract: We prove the well posedness (existence and uniqueness) of renormalized entropy solutions to the Cauchy problem for quasilinear anisotropic degenerate parabolic equations with $L^1$ data. This paper complements the work by Chen and Perthame \cite{ChenPerthame}, who developed a pure $L^1$ theory based on the notion of kinetic solutions.

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Mostafa Bendahmane, <>
Kenneth H. Karlsen, <>
Publishing information:
Revised version submitted on June 10 2003.
In this revised version we have removed the assumption that \sigma should be continuous, eq. (1.3). To this end, we have modified the arguments on pages 13 to 16 regarding the E_1 term.
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<> June 2 2003.

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