A free boundary problem for the heat equation with prescribed flux at both fixed face and melting interface

Author:
B. Sherman

Journal:
Quart. Appl. Math. **25** (1967), 53-63

MSC:
Primary 80.00

DOI:
https://doi.org/10.1090/qam/213104

MathSciNet review:
213104

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References | Similar Articles | Additional Information

**[1]**B. A. Boley and J. H. Weiner,*Theory of thermal stresses*, Wiley, New York, 1950 MR**0112414****[2]**S. J. Citron,*Heat conduction in a melting slab*, J. Aero/Space Sciences**27**, 219-228 (1960) MR**0111468****[3]**J. Douglas,*A uniqueness theorem for the solution of a Stefan problem*, Proc. Amer. Math. Soc.**8**, 402-408 (1957) MR**0092086****[4]**A. Friedman,*Free boundary problems for parabolic equations*. I, II, III, J. Math. Mech.**8**, 483-498 (1959); ibid.**9**, 19-66 (1960); ibid.**9**, 327-345 (1960)**[5]**A. Friedman,*Remarks on Stefan-type free boundary problems for parabolic equations*, J Math. Mech.**9**, 885-903 (1960) MR**0144081****[6]**A. Friedman,*Partial differential equations of parabolic type*, Prentice-Hall, Englewood Cliffs, N. J., 1964 MR**0181836****[7]**I. I. Kolodner,*Free boundary problems for the heat equation with applications to problems of change of phase*, Comm. Pure Appl. Math.**9**, 1-31 (1956) MR**0087011****[8]**W. T. Kyner,*On a free boundary value problem for the heat equation*, Quart. Appl. Math.**17**, 305-310 (1959) MR**0123843****[9]**W. T. Kyner,*An existence and uniqueness theorem for a non-linear Stefan problem*, J. Math. Mech.**8**, 483-498 (1959) MR**0144082****[10]**H. G. Landau,*Heat conduction in a melting solid*, Quart. Appl. Math.**8**, 8l-94 (1950) MR**0033441****[11]**W. L. Miranker,*A free boundary value problem for the heat equation*, Quart. Appl. Math.**16**, 121-130 (1958) MR**0094136****[12]**L. Nirenberg,*A strong maximum principle for parabolic equations*, Comm. Pure Appl. Math.**6**, 167-177 (1953) MR**0055544****[13]**B. Sherman,*A free boundary problem for the heat equation with heat input at a melting interface*, Quart. Appl. Math.**23**, 337-347 (1966) MR**0190554**

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DOI:
https://doi.org/10.1090/qam/213104

Article copyright:
© Copyright 1967
American Mathematical Society