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Well-posedness of the Dirichlet problem for the non-linear diffusion equation in non-smooth domains.
- Source :
-
Transactions of the American Mathematical Society . Jan2005, Vol. 357 Issue 1, p247-265. 19p. - Publication Year :
- 2005
-
Abstract
- We investigate the Dirichlet problem for the parablic equation [ u_t = \Delta u^m, m > 0, \] in a non-smooth domain $\Omega \subset \mathbb{R}^{N+1}, N \geq 2$. In a recent paper [{\em 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 $L_1$-contraction estimation in general non-smooth domains. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIRICHLET problem
*BOUNDARY value problems
*MATHEMATICS
*SCIENCE
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 357
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 15263910
- Full Text :
- https://doi.org/10.1090/S0002-9947-04-03464-6