A free boundary problem for the heat equation with prescribed flux at both fixed face and melting interface

Sherman, B.

doi:10.1090/qam/213104

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
Full-text PDF Free Access

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