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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
97/2003

Reaction-Diffusion in Nonsmooth and Closed Domains

Ugur G. Abdulla

Abstract

We investigate the Dirichlet problem for the parabolic equation \[ u_t = \Delta u^m-bu^\beta, m > 0, \beta > 0, b \in R \] in a non-smooth and closed domain $\Omega \subset R^{N+1}, N \geq 2$ possibly formed with irregular surfaces and having a characteristic vertex point. Existence, boundary regularity, uniqueness and comparison results are established.

Received:
Nov 28, 2003
Published:
Nov 28, 2003
MSC Codes:
35K65, 35K55
Keywords:
reaction-diffusion, nonsmooth domains, boundary regularity, boundary gradient estimates, degenerate and singular parabolic equations, uniqueness and comparison results

Related publications

inJournal
2007 Journal Open Access
Ugur G. Abdulla

Reaction-diffusion in nonsmooth and closed domains

In: Boundary value problems, 2007 (2007), p. 31261