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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.

Nov 28, 2003
Nov 28, 2003
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