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Dual extremum principles for the heat equation†

Published online by Cambridge University Press:  14 February 2012

W. D. Collins
W. D. Collins
Affiliation:
Department of Applied Mathematics and Computing Science, University of Sheffield
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Synopsis

Dual extremum principles characterising the solution of initial value problems for the heat equation are obtained by imbedding the problem in a two-point boundary-value problem for a system in which the original equation is coupled with its adjoint. Bounds on quantities of interest in the original initial value problem are obtained. Such principles are examples of ones which can be obtained for a general class of linear operators on a Hilbert space.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 3-4 , 1977 , pp. 273 - 292
Copyright
Copyright © Royal Society of Edinburgh 1977

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