Preprint 40/2000

Well-posedness of the Dirichlet Problem for the Nonlinear Diffusion Equation in Non-smooth Domains

Ugur G. Abdulla

Contact the author: Please use for correspondence this email.
Submission date: 05. Jun. 2000
Pages: 25
published in: Transactions of the American Mathematical Society, 357 (2005) 1, p. 247-265 
DOI number (of the published article): 10.1090/S0002-9947-04-03464-6
MSC-Numbers: 35K65, 35K55
Keywords and phrases: dirichlet problem, non-smooth domains, nonlinear diffusion, degenerate and singular parabolic equations, uniqueness and comparison results, l1-contraction, boundary gradient estimates

Abstract:
We investigate the Dirichlet problem for the parablic equation

displaymath38

in a non-smooth domain tex2html_wrap_inline40. In a recent paper [1] 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 tex2html_wrap_inline42-contraction estimation in general non-smooth domains.

29.11.2012, 16:37