Well-posedness of the Dirichlet Problem for the Non-linear Diffusion Equation in Non-smooth Domains
نویسنده
چکیده
We investigate the Dirichlet problem for the parablic equation ut = ∆u , m > 0, in a non-smooth domain Ω ⊂ RN+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 and comparison theorems and results on the continuous dependence of the solution on the initial-boundary data. In particular, we prove L1-contraction estimation in general non-smooth domains.
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تاریخ انتشار 2004