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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions
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by L. E. Payne and G. A. Philippin PDF
Proc. Amer. Math. Soc. 141 (2013), 2309-2318 Request permission

Abstract:

A class of initial boundary value problems for the semilinear heat equation with time dependent coefficients is considered. Using a first order differential inequality technique, the influence of the data on the behaviour of the solutions (blow-up in finite or infinite time, global existence) is investigated. Lower and upper bounds are derived for the blow-up time when blow-up occurs.
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Additional Information
  • L. E. Payne
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
  • G. A. Philippin
  • Affiliation: Département de Mathématiques et de Statistique, Université Laval, Québec, Canada G1V 0A6
  • Email: gphilip@mat.ulaval.ca
  • Received by editor(s): July 9, 2011
  • Received by editor(s) in revised form: October 9, 2011
  • Published electronically: February 20, 2013
  • Communicated by: Michael Hitrik
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 2309-2318
  • MSC (2010): Primary 35K55, 35K61, 35B30, 35B44
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11493-0
  • MathSciNet review: 3043012