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]**Jim Douglas Jr.,*A uniqueness theorem for the solution of a Stefan problem*, Proc. Amer. Math. Soc.**8**(1957), 402–408. MR**0092086**, https://doi.org/10.1090/S0002-9939-1957-0092086-6**[3]**Jim 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**(1955), 557–571. MR**0078755****[4]**Avner Friedman,*Free boundary problems for parabolic equations. I. Melting of solids.*, J. Math. Mech.**8**(1959), 499–517. MR**0144078****[5]**Avner Friedman,*Remarks on Stefan-type free boundary problems for parabolic equations.*, J. Math. Mech.**9**(1960), 885–903. MR**0144081****[6]**Avner Friedman,*Partial differential equations of parabolic type*, Prentice-Hall, Inc., 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**(1959), 483–498. MR**0144082****[8]**Walter T. Kyner,*On a free boundary value problem of the heat equation*, Quart. Appl. Math.**17**(1959), 305–310. MR**0123843**, https://doi.org/10.1090/S0033-569X-1959-0123843-6**[9]**W. L. Miranker,*A free boundary value problem for the heat equation*, Quart. Appl. Math.**16**(1958), 121–130. MR**0094136**, https://doi.org/10.1090/S0033-569X-1958-94136-6**[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**(1967), 53–63. MR**0213104**, https://doi.org/10.1090/S0033-569X-1967-0213104-3**[11]**B. Sherman,*Continuous dependence and differentiability properties of the solution of a free boundary problem for the heat equation*, Quart. Appl. Math.**27**(1969/70), 427–439. MR**0509051**, https://doi.org/10.1090/S0033-569X-1970-0509051-2**[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.**33**(1971), 449–466. MR**0274975**, https://doi.org/10.1016/0022-247X(71)90070-9**[13]**B. Sherman,*Limiting behavior in some Stefan problems as the latent heat goes to zero*, SIAM J. Appl. Math.**20**(1971), 319–327. MR**0293259**, https://doi.org/10.1137/0120034**[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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DOI:
https://doi.org/10.1090/qam/282082

Article copyright:
© Copyright 1970
American Mathematical Society