Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Thermomechanics and the formulation of the Stefan problem for fully faceted interfaces

Authors: Morton E. Gurtin and José Matias
Journal: Quart. Appl. Math. 53 (1995), 761-782
MSC: Primary 35R35; Secondary 35Q72, 73B30, 80A22
DOI: https://doi.org/10.1090/qam/1359510
MathSciNet review: MR1359510
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Abstract: This paper develops a thermomechanics of two-phase heat conductors in which the interface between phases is fully faceted. The theory is based on balance of forces, balance of energy, and growth of entropy in conjunction with constitutive equations for the interface; and the chief result is a free-boundary problem of Stefan type in which the classical interface condition $ u = 0$ is replaced by a condition relating the integral of $ u$ over each facet to the normal velocity of that facet.

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DOI: https://doi.org/10.1090/qam/1359510
Article copyright: © Copyright 1995 American Mathematical Society

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