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Online ISSN 1552-4485; Print ISSN 0033-569X
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
- H. G. Landau, Heat conduction in a melting solid, Quart. Appl. Math. 8 (1950), 81–94. MR 33441, DOI https://doi.org/10.1090/S0033-569X-1950-33441-3
- Bruno A. Boley and Jerome H. Weiner, Theory of thermal stresses, John Wiley & Sons, Inc., New York London, 1960. MR 0112414
- Bruno A. Boley, A method of heat conduction analysis of melting and solidification problems, J. Math. and Phys. 40 (1961), 300–313. MR 141376
- Bruno A. Boley, Upper and lower bounds for the solution of a melting problem, Quart. Appl. Math. 21 (1963), 1–11. MR 147124, DOI https://doi.org/10.1090/S0033-569X-1963-0147124-3
- Stephen J. Citron, Heat conduction in a melting slab, J. Aero/Space Sci. 27 (1960), 219–228. MR 111468
- 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 43330, DOI https://doi.org/10.1090/S0033-569X-1951-43330-2
- W. L. Miranker, A free boundary value problem for the heat equation, Quart. Appl. Math. 16 (1958), 121–130. MR 94136, DOI https://doi.org/10.1090/S0033-569X-1958-94136-6
- Walter T. Kyner, On a free boundary value problem of the heat equation, Quart. Appl. Math. 17 (1959), 305–310. MR 123843, DOI https://doi.org/10.1090/S0033-569X-1959-0123843-6
- W. T. Kyner, An existence and uniqueness theorem for a nonlinear Stefan problem., J. Math. Mech. 8 (1959), 483–498. MR 0144082, DOI https://doi.org/10.1512/iumj.1959.8.58035 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)
- Avner Friedman, Remarks on Stefan-type free boundary problems for parabolic equations., J. Math. Mech. 9 (1960), 885–903. MR 0144081, DOI https://doi.org/10.1512/iumj.1960.9.59053
- William F. Trench, On an explicit method for the solution of a Stefan problem, J. Soc. Indust. Appl. Math. 7 (1959), 184–204. MR 110205
- 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 78755
- 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 87011, DOI https://doi.org/10.1002/cpa.3160090102 E. Goursat, Cours d’analyse mathiéalique, vol. 3, Gauthier-Villars, Paris, 1927, (English translation issued by Dover, 1964)
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Article copyright:
© Copyright 1966
American Mathematical Society