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

Published online by Cambridge University Press:  07 June 2012

L. E. Payne  and
G. A. Philippin
L. E. Payne
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
G. A. Philippin
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec G1K 7P4, Canada ([email protected])
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Abstract

This paper deals with the blow-up of solutions to a class of parabolic problems with time-dependent coefficients under homogeneous Neumann boundary conditions. For one set of problems in this class we show that no global solution can exist. For another we derive lower bounds for the time of blow-up when blow-up occurs.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 3 , June 2012 , pp. 625 - 631
Copyright
Copyright © Royal Society of Edinburgh 2012

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