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

Tarzia, Domingo Alberto; Turner, Cristina Vilma

doi:10.1090/qam/1146619

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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