A free boundary problem for the heat equation with heat input at a melting interface

Author:
B. Sherman

Journal:
Quart. Appl. Math. **23** (1966), 337-347

MSC:
Primary 35.78

DOI:
https://doi.org/10.1090/qam/190554

MathSciNet review:
190554

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**[1]**H. G. Landau,*Heat conduction in a melting solid*, Quart. Appl. Math.**8**(1950), 81–94. MR**0033441**, https://doi.org/10.1090/S0033-569X-1950-33441-3**[2]**Bruno A. Boley and Jerome H. Weiner,*Theory of thermal stresses*, John Wiley & Sons, Inc., New York London, 1960. MR**0112414****[3]**Bruno A. Boley,*A method of heat conduction analysis of melting and solidification problems*, J. Math. and Phys.**40**(1961), 300–313. MR**0141376****[4]**Bruno A. Boley,*Upper and lower bounds for the solution of a melting problem*, Quart. Appl. Math.**21**(1963), 1–11. MR**0147124**, https://doi.org/10.1090/S0033-569X-1963-0147124-3**[5]**Stephen J. Citron,*Heat conduction in a melting slab*, J. Aero/Space Sci.**27**(1960), 219–228. MR**0111468****[6]**G. W. Evans II,*A note on the existence of a solution to a problem of Stefan*, Quart. Appl. Math.**9**(1951), 185–193. MR**0043330**, https://doi.org/10.1090/S0033-569X-1951-43330-2**[7]**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**[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. T. Kyner,*An existence and uniqueness theorem for a nonlinear Stefan problem.*, J. Math. Mech.**8**(1959), 483–498. MR**0144082****[10]**A. Friedman,*Free boundary problems for parabolic equations*. I, II, III, J. of Math, and Mech.**8**, 499-517 (1959); ibid.**9**, 19-66 (1960); ibid.**9**, 327-345 (1960)**[11]**Avner Friedman,*Remarks on Stefan-type free boundary problems for parabolic equations.*, J. Math. Mech.**9**(1960), 885–903. MR**0144081****[12]**William F. Trench,*On an explicit method for the solution of a Stefan problem*, J. Soc. Indust. Appl. Math.**7**(1959), 184–204. MR**0110205****[13]**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****[14]**I. I. Kolodner,*Free boundary problem for the heat equation with applications to problems of change of phase. I. General method of solution*, Comm. Pure Appl. Math.**9**(1956), 1–31. MR**0087011**, https://doi.org/10.1002/cpa.3160090102**[15]**E. Goursat,*Cours d'analyse mathiéalique*, vol. 3, Gauthier-Villars, Paris, 1927, (English translation issued by Dover, 1964)

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DOI:
https://doi.org/10.1090/qam/190554

Article copyright:
© Copyright 1966
American Mathematical Society