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 $k(x)f(u)$.

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Steinar Evje
Kenneth Hvistendahl Karlsen, <>
Nils Henrik Risebro, <>
Publishing information:
Submitted to Proc. Hyp 2000
Submitted by:
<> May 31 2000.

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