A general one-phase Stefan problem

Author:
B. Sherman

Journal:
Quart. Appl. Math. **28** (1970), 377-382

MSC:
Primary 35.78; Secondary 80.00

DOI:
https://doi.org/10.1090/qam/282082

MathSciNet review:
282082

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References | Similar Articles | Additional Information

**[1]**H. Chernoff,*Sequential tests for the mean of a normal distribution*, Proc. Fourth Berkeley Sympos.**1**, 79-92 (1961); II (large ) (with J. Breakwell), Ann. Math. Statist.**35**, 162-173 (1964); III (small ), ibid.**36**, 28-54 (1965); IV (discrete case), ibid.**36**, 55-68 (1965)**[2]**J. Douglas,*A uniqueness theorem for the solution of a Stefan problem*, Proc. Amer. Math. Soc.**8**, 402-408 (1957) MR**0092086****[3]**J. Douglas, Jr. and T. M. Gallie, Jr.,*On the numerical integration of a parabolic differential equation subject to a moving boundary condition*, Duke Math. J.**22**, 557-571 (1955) MR**0078755****[4]**A. Friedman,*Free boundary problems for parabolic equations*. I, J. Math. Mech.**8**, 499-518 (1959) MR**0144078****[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]**W. T. Kyner,*An existence and uniqueness theorem for a nonlinear Stefan problem*, J. Math. Mech.**8**, 483-498 (1959) MR**0144082****[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. L. Miranker,*A free boundary value problem for the heat equation*, Quart. Appl. Math.**16**, 121-130 (1958) MR**0094136****[10]**B. Sherman,*A free boundary problem for the heat equation with prescribed flux at both fixed face and melting interface*, Quart. Appl. Math.**25**, 53-63 (1967) MR**0213104****[11]**B. Sherman,*Continuous dependence and differentiability properties of the solution of a free boundary problem for the heat equation*, Quart. Appl. Math.**27**, 427-439 (1970) MR**0509051****[12]**B. Sherman,*Free boundary problems for the heat equation in which the moving interface coincides initially with the fixed face*, J. Math. Anal. Appl. (to appear) MR**0274975****[13]**B. Sherman,*Limiting bahavior in two Stefan problems as the latent heat goes to zero*, SIAM J. Appl. Math. (to appear) MR**0293259****[14]**T. D. Wentzel,*A free boundary problem for the heal equation*, Dokl. Akad. Nauk SSSR**131**, 1000-1003 (1960) Soviet Math. Dokl.**1**, 358-361 (1960)

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Additional Information

DOI:
https://doi.org/10.1090/qam/282082

Article copyright:
© Copyright 1970
American Mathematical Society