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Bounds for blow-up time for the heat equation under nonlinear boundary conditions

Published online by Cambridge University Press:  04 November 2009

L. E. Payne  and
P. W. Schaefer
L. E. Payne
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA, ([email protected])
P. W. Schaefer
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37916, USA ([email protected])
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Abstract

A differential inequality technique is used to determine a lower bound on the blow-up time for solutions to the heat equation subject to a nonlinear boundary condition when blow-up of the solution does occur. In addition, a sufficient condition which implies that blow-up does occur is determined.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 6 , December 2009 , pp. 1289 - 1296
Copyright
Copyright © Royal Society of Edinburgh 2009

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