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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
40/2000

Well-posedness of the Dirichlet Problem for the Nonlinear Diffusion Equation in Non-smooth Domains

Ugur G. Abdulla

Abstract

We investigate the Dirichlet problem for the parablic equation $$ u_t = \Delta u^m, m > 0, $$ in a non-smooth domain $\Omega \subset \mathbb{R}^{N+1}, N \ge 2$. In a recent paper [U.G. Abdulla, J. Math. Anal. Appl., 260, 2 (2001), 384-403] 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.

Received:
Jun 5, 2000
Published:
Jun 5, 2000
MSC Codes:
35K65, 35K55
Keywords:
dirichlet problem, non-smooth domains, nonlinear diffusion, degenerate and singular parabolic equations, uniqueness and comparison results, l1-contraction, boundary gradient estimates

Related publications

inJournal
2005 Repository Open Access
Ugur G. Abdulla

Well-posedness of the Dirichlet problem for the non-linear diffusion equation in non-smooth domains

In: Transactions of the American Mathematical Society, 357 (2005) 1, pp. 247-265