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Uniqueness of a Nonmonotone Free Boundary Problem

C. Y. Chan
SIAM Journal on Applied Mathematics
Vol. 20, No. 2 (Mar., 1971), pp. 189-194
Stable URL: http://www.jstor.org/stable/2099920
Page Count: 6
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Uniqueness of a Nonmonotone Free Boundary Problem
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Abstract

A finite slab of solid is in contact with its liquid of finite length. Heat is taken away from the free end of the solid while temperature is prescribed at the free end of the liquid which is removed at an arbitrary rate. The solution of this nonmonotone free boundary problem is shown to be unique by construction through the use of the comparison lemmas. The cases when initially only one phase is present are also established. Other types of boundary conditions are also considered.

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