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Applicable Analysis
An International Journal
Volume 85, 2006 - Issue 10
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Original Articles

Lower bounds for blow-up time in parabolic problems under Neumann conditions

L. E. Payne Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
&
P. W. Schaefer Department of Mathematics, University of Tennessee, Knoxville, TN 37916, USACorrespondence[email protected]
Pages 1301-1311 | Accepted 09 Jun 2006, Published online: 17 Feb 2007
 
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Abstract

We consider an initial boundary value problem for the semilinear heat equation under homogeneous Neumann boundary conditions in which the solution may blow up in finite time. A lower bound for the blow-up time is determined by means of a differential inequality argument when blow up occurs. Under alternative conditions on the nonlinearity, some additional bounds for blow-up time are also determined.

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