We study the degenerate differential equation
with the initial condition on and boundary condition on some part of the boundary with a.e. on . The vector field is assumed to satisfy the Leray-Lions conditions, and the functions to be continuous, locally Lipschitz, nondecreasing and to satisfy the normalization condition and the range condition . We assume also that has a flat region with . Using Kruzhkov's method of doubling variables, we prove an existence and comparison result for renormalized entropy solutions.
Submitted August 15, 2009. Published November 20, 2009.
Math Subject Classifications: 35K55, 35J65, 35J70, 35B30.
Key Words: Renormalized; degenerate; diffusion; homogenous boundary conditions; continuous flux.
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| Kaouther Ammar |
TU Berlin, Institut für Mathematik, MA 6-3
Strasse des 17. Juni 136, 10623 Berlin, Germany
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