Nonlinear Diffusion in Irregular Domains

Ugur G. Abdulla

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Submission date: 01. Aug. 2001
Pages: 28
published in: Elliptic and parabolic problems
River Edge, NJ [u.a.] : World Scientific, 2002. - P. 302 - 310 
Bibtex
MSC-Numbers: 35K65, 35K55
Keywords and phrases: dirichlet problem, non-smooth domains, nonlinear diffusion, degenerate and singular parabolic equations, uniqueness and comparison results, l1-contraction, boundary gradient estimates

Abstract:
We investigate the Dirichlet problem for the parablic equation


in a non-smooth domain . In a recent paper [U.G.Abdulla, J. Math. Anal. Appl., 260, 2 (2001)] existence and boundary regularity results were established. In this paper we present uniqueness and comparison theorems and results on the continuous dependence of the solution on the initial-boundary data. In particular, we prove -contraction estimation in general non-smooth domains.