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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
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA, (lep8@cornell.edu)
P. W. Schaefer
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37916, USA (schaefer@math.utk.edu)

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
Copyright
Copyright © Royal Society of Edinburgh 2009

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