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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions


Authors: L. E. Payne and G. A. Philippin
Journal: Proc. Amer. Math. Soc. 141 (2013), 2309-2318
MSC (2010): Primary 35K55, 35K61, 35B30, 35B44
Published electronically: February 20, 2013
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11493-0
PII: S 0002-9939(2013)11493-0
Keywords: Parabolic problems, blow-up.
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.