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Bounds on solutions of one-phase Stefan problems

Published online by Cambridge University Press:  26 September 2008

A. A. Lacey
A. A. Lacey
Affiliation:
Department of Mathematics. Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland
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Abstract

The reformulation of one-phase Stefan problems, by use of a Baiocchi-type transformation, as ‘oxygen-diffusion’ problems, makes it possible to compare different solutions. The comparison extends to ‘zero-specific-heat’ cases, which are better known, in two dimensions, as Hele-Shaw problems. Known solutions of Hele-Shaw problems can be used to bound and estimate asymptotic behaviour of solutions to Stefan problems. The use of similar techniques gives rise to some exact solutions of ‘squeeze-film’ problems and some limited results concerning continuity.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 5 , October 1995 , pp. 509 - 516
Copyright
Copyright © Cambridge University Press 1995

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