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Existence and continuity of a weak solution to the problem of a free boundary in a concentrated capacity

Published online by Cambridge University Press:  14 November 2011

M. Shillor
M. Shillor
Affiliation:
Mathematical Institute, Oxford University, Oxford
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Synopsis

A weak (enthalpy) formulation of the problem of a free boundary moving in the thermal concentrated capacity is given. The problem is to solve the heat equation in a given domain, while on a part of the boundary of this domain the solution (or rather its trace) solves a Stefan problem with forced convection. The existence of a global weak solution is proved by the method of finite differences. Some regularity is obtained from this proof, and the continuity of the temperature is proved. The uniqueness, which is related to the existence of mushy regions, is discussed. A classical enthalpy formulation is conjectured.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 3-4 , 1985 , pp. 271 - 280
Copyright
Copyright © Royal Society of Edinburgh 1985

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