Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The Stefan problem with a convective boundary condition


Authors: A. D. Solomon, V. Alexiades and D. G. Wilson
Journal: Quart. Appl. Math. 40 (1982), 203-217
MSC: Primary 35R35; Secondary 35B30, 80A20
DOI: https://doi.org/10.1090/qam/666675
MathSciNet review: 666675
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Abstract: We study the one-phase Stefan problem on a semi-infinite strip $ x \ge 0$, with the convective boundary condition $ - K{T_x}\left( {0, t} \right) = h\left[ {{T_L} - T(0, t)} \right]$. Points of interest include: a) behavior of the surface temperature $ T\left( {0, t} \right)$; b) asymptotic behavior as $ h \to \infty $; c) uniqueness, and d) bounds on the phase change front and total system energy.


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DOI: https://doi.org/10.1090/qam/666675
Article copyright: © Copyright 1982 American Mathematical Society


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