Well-posedness of the Dirichlet problem for the non-linear diffusion equation in non-smooth domains

Author:
Ugur G. Abdulla

Translated by:

Journal:
Trans. Amer. Math. Soc. **357** (2005), 247-265

MSC (2000):
Primary 35K65, 35K55

DOI:
https://doi.org/10.1090/S0002-9947-04-03464-6

Published electronically:
February 27, 2004

MathSciNet review:
2098094

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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the Dirichlet problem for the parablic equation

in a non-smooth domain . 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 -contraction estimation in general non-smooth domains.

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Additional Information

**Ugur G. Abdulla**

Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, 150 West University Boulevard, Melbourne, Florida 32901-6975

Email:
abdulla@fit.edu

DOI:
https://doi.org/10.1090/S0002-9947-04-03464-6

Keywords:
Dirichlet problem,
non-smooth domains,
non-linear diffusion,
degenerate and singular parabolic equations,
uniqueness and comparison results,
$L_1$-contraction,
boundary gradient estimates.

Received by editor(s):
July 31, 2000

Received by editor(s) in revised form:
July 21, 2003

Published electronically:
February 27, 2004

Article copyright:
© Copyright 2004
American Mathematical Society