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Online ISSN 1552-4485; Print ISSN 0033-569X
A free boundary problem for the heat equation with prescribed flux at both fixed face and melting interface
Author:
B. Sherman
Journal:
Quart. Appl. Math. 25 (1967), 53-63
MSC:
Primary 80.00
DOI:
https://doi.org/10.1090/qam/213104
MathSciNet review:
213104
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References | Similar Articles | Additional Information
- Bruno A. Boley and Jerome H. Weiner, Theory of thermal stresses, John Wiley & Sons, Inc., New York London, 1960. MR 0112414
- Stephen J. Citron, Heat conduction in a melting slab, J. Aero/Space Sci. 27 (1960), 219–228. MR 111468
- Jim Douglas Jr., A uniqueness theorem for the solution of a Stefan problem, Proc. Amer. Math. Soc. 8 (1957), 402–408. MR 92086, DOI https://doi.org/10.1090/S0002-9939-1957-0092086-6 A. Friedman, Free boundary problems for parabolic equations. I, II, III, J. Math. Mech. 8, 483–498 (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
- Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0181836
- 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
- 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
- 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
- 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
- Louis Nirenberg, A strong maximum principle for parabolic equations, Comm. Pure Appl. Math. 6 (1953), 167–177. MR 55544, DOI https://doi.org/10.1002/cpa.3160060202
- B. Sherman, A free boundary problem for the heat equation with heat input at a melting interface, Quart. Appl. Math. 23 (1965/66), 337–348. MR 190554, DOI https://doi.org/10.1090/S0033-569X-1966-0190554-6
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Article copyright:
© Copyright 1967
American Mathematical Society