We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
48/2001
Nonlinear Diffusion in Irregular Domains
Ugur G. Abdulla
Abstract
We investigate the Dirichlet problem for the parablic equation $$u_i = \Delta u^m,m>0$$ in a non-smooth domain $\Omega \subset \mathbb{R}^{N+1} ,N\geq 2$. 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 $L_1$-contraction estimation in general non-smooth domains.
