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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.
