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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Well-posedness of the Dirichlet problem for the non-linear diffusion equation in non-smooth domains
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by Ugur G. Abdulla PDF
Trans. Amer. Math. Soc. 357 (2005), 247-265 Request permission

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 [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.
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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
  • Received by editor(s): July 31, 2000
  • Received by editor(s) in revised form: July 21, 2003
  • Published electronically: February 27, 2004
  • © Copyright 2004 American Mathematical Society
  • 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
  • MathSciNet review: 2098094