Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



A note on the existence of a waiting time for a two-phase Stefan problem

Authors: Domingo Alberto Tarzia and Cristina Vilma Turner
Journal: Quart. Appl. Math. 50 (1992), 1-10
MSC: Primary 35R35; Secondary 35K05
DOI: https://doi.org/10.1090/qam/1146619
MathSciNet review: MR1146619
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Abstract: We consider a slab, represented by the interval $ 0 < x < {x_0}$, at the initial temperature $ {\theta _0} = {\theta _0}\left( x \right) \ge 0\left( {or {\phi _0} = {\phi _0}\left( x \right) \ge 0} \right)$ having a heat flux $ q = q\left( t \right) > 0$ (or convective boundary condition with a heat transfer coefficient $ h$) on the left face $ x = 0$ and a temperature condition $ b\left( t \right) > 0$ on the right face $ x = {x_0}$ ($ x_{0}$ could be also $ + \infty $, i.e., a semi-infinite material). We consider the corresponding heat conduction problem and assume that the phase-change temperature is $ {0^ \circ }C$.

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DOI: https://doi.org/10.1090/qam/1146619
Article copyright: © Copyright 1992 American Mathematical Society

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