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Energy and pointwise bounds in some non-standard parabolic problems

Published online by Cambridge University Press:  12 July 2007

K. A. Ames ,
L. E. Payne  and
P. W. Schaefer
K. A. Ames
Affiliation:
Department of Mathematical Sciences, University of Alabama, Huntsville, AL 35899, USA([email protected])
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

We study a class of initial-boundary-value problems for which an auxiliary condition of the form is prescribed. We determine bounds on an energy expression by means of differential inequalities and derive pointwise bounds for the solution and its gradient by use of a parabolic maximum principle.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 1 , February 2004 , pp. 1 - 9
Copyright
Copyright © Royal Society of Edinburgh 2004

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