### 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