Preprint 2000015
On the Uniqueness and Stability of Entropy Solutions of Nonlinear
Degenerate Parabolic Equations with Rough Coefficients
Kenneth Hvistendahl Karlsen and Nils Henrik Risebro
Abstract:
We study nonlinear degenerate parabolic equations where the
flux function $f(x,t,u)$ does not depend Lipschitz
continuously on the spatial location $x$.
By properly adapting the ``doubling of variables'' device due
to Kru\v{z}kov \cite{Kruzkov} and Carrillo \cite{Carrillo}, we prove
a uniqueness result within the class of
entropy solutions for the initial value problem.
We also prove a result concerning the continuous dependence
on the initial data and the flux function for degenerate
parabolic equations with flux function of the form
$k(x)f(u)$, where $k(x)$ is a vectorvalued function
and $f(u)$ is a scalar function.
 Paper:
 Available as PDF.
 Author(s):
 Kenneth Hvistendahl Karlsen,
<kennethk@mi.uib.no>
 Nils Henrik Risebro,
<nilshr@math.uio.no>
 Publishing information:

 Comments:
 Preprint updated December 8, 2000.
 Submitted by:

<kennethk@mi.uib.no>
April 28 2000.
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Last modified: Fri Dec 8 10:07:52 MET 2000