Preprint 2001008
An error estimate for viscous approximate solutions of degenerate parabolic equations
Steinar Evje and Kenneth H. Karlsen
Abstract:
Relying on recent advances in the theory of entropy
solutions for nonlinear (strongly) degenerate parabolic
equations, we present a direct proof
of an L^{1} error estimate for
viscous approximate
solutions of the initial value problem for
$\pt w+\Div \bigl(V(x)f(w)\bigr) = \Delta A(w)$, where
$V=V(x)$ is a vector field, $f=f(u)$ is a scalar function,
and $A'(\cdot)\ge 0$. The viscous approximate
solutions are weak solutions of the initial value problem for
the uniformly parabolic equation
$\pt w^{\eps}+\Div \bigl(V(x)f(w^{\eps})\bigr) =
\Delta \bigl(A(w^{\eps}) +\eps w^{\eps}\bigr)$, $\eps>0$.
The error estimate is of order $\sqrt{\eps}$.
 Paper:
 Available as PostScript (261 Kbytes) or
gzipped PostScript (98 Kbytes; uncompress
using gunzip).
 Author(s):
 Steinar Evje,
<Steinar.Evje@rf.no>
 Kenneth H. Karlsen,
<kennethk@mi.uib.no>
 Publishing information:
 UCLA Computational and Applied Mathematics Report.
 Comments:

 Submitted by:

<kennethk@mi.uib.no>
February 15 2001.
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