MiS Preprint Repository

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 ( 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

Reaction-Diffusion in Nonsmooth and Closed Domains

Ugur G. Abdulla


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.

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

Related publications

2007 Journal Open Access
Ugur G. Abdulla

Reaction-diffusion in nonsmooth and closed domains

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