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Free boundary problems of Stephan type with prescribed flux. (English) Zbl 0271.35038


MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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[1] Budak, B. M.; Vasilév, F. F.; Uspenskil̆, A. B., Difference methods for solving certain boundary value problems of Stephan type, (Num. Meth. in Gas. Dynamics (1965), Izdat. Moskov. Univ: Izdat. Moskov. Univ Moscow), 139-183, (Russian)
[2] Cannon, J. R.; Hill, C. D., Existence, uniqueness, stability, and monotone dependence in a Stephan problem for the heat equation, J. Math. Mech., 17, No. 12 (1967) · Zbl 0154.36403
[3] Cannon, J. R.; Hill, C. D.; Douglas, A multiphase Stephan problem, J. Math. Mech., 17, No. 12 (1967) · Zbl 0154.36501
[4] Cannon, J. R.; Hill, C. D., On the infinite differentiability of the free boundary in a Stephan problem, (Technical Report No. 806 (Nov. 1967), M.R.C., University of Wisconsin) · Zbl 0154.36403
[5] H. Chernoff1; H. Chernoff1
[6] Friedman, A., Free boundary problems for parabolic equations I. Melting of solids, J. Math. Mech., 8, 499-518 (1959) · Zbl 0089.07801
[7] Friedman, A., Partial Differential Equations of Parabolic Type (1964), Prentice Hall, Inc: Prentice Hall, Inc Englewood Cliffs, New Jersey · Zbl 0144.34903
[8] Greenberg, J. M., A free boundary problem for the linear heat equation, (Technical Report (June 1968), Carnegie-Mellon Institute: Carnegie-Mellon Institute Pittsburgh, Pennsylvania) · Zbl 0205.10004
[9] Nguyen Dinh, Thi, On a free boundary problem for parabolic equations, Moscow Univ. Vestnik, Ser. 1. Matematika, Mekhanika, No. 2, 40-54 (1966)
[10] Kolodner, I., Free boundary problems for the heat equation with applications to change of phase, Comm. Pure Appl. Math., 9, 1-31 (1966) · Zbl 0070.43803
[11] Kyner, W. T., An Existence and uniqueness theorem for a nonlinear Stephan problem, J. Math. Mech., 8, 483-498 (1959) · Zbl 0087.09301
[12] McKean, H. P., Appendix to the paper “Rational Theory of Warrant Pricing” by P. A. Samuelson, Industrial Mgt. Rev., 6, No. 2 (1965)
[13] Oleǐnik, O. A., A method of solution of the general Stephan problem, Soviet Math. Dokl., 1, 1350-1354 (1960) · Zbl 0131.09202
[14] H. M. Taylor; H. M. Taylor
[15] Vasilév, F. P., A difference method of solving problems of Stephan type for a quasi-linear parabolic equation with discontinuous coefficients, Soviet Math. Dokl., \(5^2, 1109-1113 (1964)\) · Zbl 0168.08401
[16] H. Chernoff; H. Chernoff · Zbl 0188.47801
[17] Friedman, A., The Stephan problem in many dimensions, Trans. Am. Math. Soc., 133, 51-89 (1968)
[18] Friedman, A., One dimensional Stephan problems with nonmonotone free boundary, Trans. Am. Math. Soc., 133, 89-115 (1968) · Zbl 0162.42001
[19] Wentzel, T. D., A free boundary problem for the heat equation, Soviet Math. Dokl., 1, 358-360 (1960) · Zbl 0100.09204
[20] Sherman, B., A free boundary problem for the heat equation with prescribed flux at both fixed face and melting interface, Quarterly of Appl. Math., 25 (1967) · Zbl 0158.11904
[21] B. Sherman; B. Sherman
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