Nonlinear diffusion in irregular domains
Ugur G. Abdulla · 2002
We investigate the Dirichlet problem for the parablic equation ut = ∆um,m> 0, in a non-smooth domain Ω ⊂ IRN+1, N ≥ 2. In a recent paper [U.G.Abdulla, J. Math. Anal. Appl., 260, 2 (2001), 384-403.] existence and boundary regularity results were established. In this paper we present uniqueness, comparison and stability theorems. 1 Introduction and Statement of Main Results Consider the equation ut = ∆um (1.1) where u = u(x, t), x = (x1,..., xN) ∈ IRN, N ≥ 2, t ∈ IR+, ∆ = N∑