Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Uniqueness in a melting slab with space- and time-dependent heating

Author: Bruno A. Boley
Journal: Quart. Appl. Math. 27 (1970), 481-487
DOI: https://doi.org/10.1090/qam/254434
MathSciNet review: 254434
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Abstract: Conditions for uniqueness of solution are derived for a slab which melts under an applied heat input dependent both on time and on the melted depth, the melted material being instantaneously removed. Some examples are constructed in which more than one solution is exhibited as well as one in which no melting solution exists. A theorem demonstrating monotonic dependence of solution on boundary data under certain conditions is proved.

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DOI: https://doi.org/10.1090/qam/254434
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society