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MiS Preprint

Nonlinear Diffusion in Irregular Domains

Ugur G. Abdulla


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

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

Related publications

2002 Repository Open Access
Ugur G. Abdulla

Nonlinear diffusion in irregular domains

In: Elliptic and parabolic problems
River Edge, NJ [u.a.] : World Scientific, 2002. - pp. 302-310