A Continuous Dependence Result for Nonlinear Degenerate Parabolic Equations with Spatially Dependent Flux Function

Abstract

We study entropy solutions of nonlinear degenerate parabolic equations of form,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,and the diffusion function A(u). This paper complements previous workk(x)f(u) [7] by two of the authors, which contained a continuous dependence result concerning the initial data and the flux function k(x)f(u).