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

Full-text PDF Free Access

References | Similar Articles | Additional Information

**[1]**H. G. Landau,*Heat conduction in a melting solid*, Quart. Appl. Math.**8**, 81-94 (1950) MR**0033441****[2]**B. A. Boley and J. H. Weiner,*Theory of thermal stresses*, John Wiley and Sons, New York, 1950 MR**0112414****[3]**B. A. Boley,*A method of heat conduction analysis of melting and solidification problems*, J. of Math, and Phys.**40**, 300-313 (1961) MR**0141376****[4]**B. A. Boley,*Upper and lower bounds for the solution of a melting problem*, Quart. Appl. Math.**21**, 1-11 (1963) MR**0147124****[5]**S. J. Citron,*Heat conduction in a melting slab*, J. of the Aero/Space Sciences**27**, 219-228 (1960) MR**0111468****[6]**G. W. Evans,*A note on the existence of a solution to a problem of Stefan*, Quart. Appl. Math.**9**,185-193 (1951) MR**0043330****[7]**W. L. Miranker,*A free boundary value problem for the heat equation*, Quart. Appl. Math.**16**, 121-130 (1958) MR**0094136****[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. of Math, and Mech.**8**, 483-498 (1959) 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]**A. Friedman,*Remarks on Stefan-type free boundary problems for parabolic equations*, J. of Math, and Mech.**9**, 885-903 (1960) MR**0144081****[12]**W. F. Trench,*On an explicit method for the solution of a Stefan problem*, J. Soc. Indust. Appl. Math.**7**, 184-204 (1959) MR**0110205****[13]**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**, 557-572 (1955) MR**0078755****[14]**I. I. Kolodner,*Free boundary problems for the heat equation with applications to problems of change of phase*, Comm. Pure and Appl. Math.**9**, 1-31 (1956) MR**0087011****[15]**E. Goursat,*Cours d'analyse mathiéalique*, vol. 3, Gauthier-Villars, Paris, 1927, (English translation issued by Dover, 1964)

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
35.78

Retrieve articles in all journals with MSC: 35.78

Additional Information

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

Article copyright:
© Copyright 1966
American Mathematical Society