Preprint 2000-022
A Continuous Dependence Result for Nonlinear Degenerate Parabolic
Equations with Spatially Dependent Flux Function
Steinar Evje, Kenneth Hvistendahl Karlsen, and Nils Henrik
Risebro
Abstract:
We study entropy solutions of
nonlinear degenerate parabolic equations of
form $u_t + \Div \bigl(k(x)f(u)\bigr) = \Delta A(u)$,
where $k(x)$ is a vector-valued function
and $f(u),A(u)$ are scalar functions.
We prove a result concerning the continuous dependence
on the initial data, the flux function $k(x)f(u)$,
and the diffusion function $A(u)$. This paper
complements previous work \cite{KR:Rough_Unique} by two
of the authors, which contained a
continuous dependence result concerning the
initial data and the flux function $k(x)f(u)$.
- Paper:
- Available as PostScript.
- Author(s):
- Steinar Evje
- Kenneth Hvistendahl Karlsen,
<kennethk@mi.uib.no>
- Nils Henrik Risebro,
<nilshr@math.uio.no>
- Publishing information:
- Submitted to Proc. Hyp 2000
- Comments:
-
- Submitted by:
-
<kennethk@mi.uib.no>
May 31 2000.
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Last modified: Wed May 31 17:42:13 MET DST 2000