Preprint 2003-039

Renormalized Entropy Solutions for Quasilinear Anisotropic Degenerate Parabolic Equations.

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.

Paper:

Available as PDF (264 Mbytes).

Author(s):

Mostafa Bendahmane, <mostafab@math.uio.no>

Kenneth H. Karlsen, <kennethk@mi.uib.no>

Publishing information:

Revised version submitted on June 10 2003.

Comments:

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.

Submitted by:

<kennethk@mi.uib.no> June 2 2003.