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The Stefan problem in several space variables


Author: Avner Friedman
Journal: Trans. Amer. Math. Soc. 133 (1968), 51-87
MSC: Primary 35.65
DOI: https://doi.org/10.1090/S0002-9947-1968-0227625-7
MathSciNet review: 0227625
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  • 1. A. Friedman, Free boundary problems for parabolic equations. II. Evaporation and condensation of a liquid drop, J. Math. Mech. 9 (1960), 19-66. MR 0144079 (26:1627)
  • [1] -, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, N. J., 1964. MR 0181836 (31:6062)
  • [2] -, ``Asymptotic behavior of solutions of parabolic differential equations and of integral equations'' in Symposium on differential equations and dynamical systems, Academic Press, New York, 1967. MR 0218731 (36:1815)
  • [3] L. M. Graves, The theory of functions of real variables, 2nd ed., McGraw-Hill, New York, 1956. MR 0075256 (17:717f)
  • [4] S. L. Kamenomostskaja, On Stefan's problem, Mat. Sb. 53 (95) (1965), 485-514.
  • [5] O. D. Kellogg, On the derivatives of harmonic functions on the boundary, Trans. Amer. Math. Soc. 33 (1931), 486-510. MR 1501602
  • [6] O. A. Ladyzhenskaja and N. N. Uraltseva, Boundary problems for linear and quasi-linear parabolic equations. I, II, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 5-52, 753-780.
  • [7] E. F. McShane, Extension of range of functions, Bull. Amer. Math. Soc. 40 (1934), 837-842. MR 1562984
  • [8] L. I. Rubinstein, Two-phase Stefan problem on an interval with one-phase initial state of a heat-conducting medium, Latvijas Valsts Univ. Zinātn. Raksti 58 (1964), vyp. 2, 111-148. MR 0181840 (31:6066)
  • [9] S. L. Sobolev, Applications of functional analysis in mathematical physics, Transl. Math. Monographs, Vol. 7, Amer. Math. Soc., Providence, R. I., 1963. MR 0165337 (29:2624)
  • [10] O. A. Oleinik, On the equations of the type of nonstationary filtration, Dokl. Akad. Nauk SSSR 113 (1957), 1210-1213.
  • [11] V. Glushko and S. G. Krein, Fractional powers of differential operators and inclusion theorems, Dokl. Akad. Nauk SSSR 122 (1958), 963-966. MR 0100144 (20:6578)

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DOI: https://doi.org/10.1090/S0002-9947-1968-0227625-7
Article copyright: © Copyright 1968 American Mathematical Society

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