journal article Mar 01, 2000

Classical solvability for one-dimensional, free boundary, Florin, Muskat-Verigin, and Stefan problems

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References
44
[1]
L. I. Rubinshtein,The Stefan Problem [in Russian], Riga (1967).
[2]
A. Friedman,Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, New Jersey (1964).
[3]
I. I. Danilyuk, “The Stefan problem,”Usp. Mat. Nauk,40, 133–185 (1985).
[4]
I. I. Danilyuk, “On a crystallization process in slag formation,”Math. Phys.,17, 99–111 (1975).
[5]
W. T. Kyner, “An existence and uniqueness theorem for a nonlinear Stefan problem,”J. Math. Mech.,8, 483–498 (1959).
[6]
B. Sherman, “Free boundary problems for the heat equation in which the moving interface coincides initially with the fixed face,”J. Math. Anal. Appl.,33, 449–465 (1971). 10.1016/0022-247x(71)90070-9
[7]
V. V. Pukhnachov, “On a StEfan problem arising in a model of electric explosion of conductors,” in:Trudy Seminar S. L. Sobolev (1976), pp. 69–82.
[8]
A. Fasano and M. Primicerio, “General free boundary problems for the heat equation. I, II, III,”J. Math. Anal. Appl.,57, 694–723 (1977);58, 202–231 (1977);59, 1–14 (1977). 10.1016/0022-247x(77)90256-6
[9]
A. M. Meirmanov,The Stefan Problems [in Russian], Novosibirsk (1986).
[10]
B. V. Bazalii and V. Y. Shelepov, “On asymptotic behavior of solutions of a Stefan problem,”Dokl. Akad. Nauk Ukr. SSR, 1059–1061 (1978).
[11]
B. V. Bazalii and V. Y. Shelepov, “Estimates of stabilization velocity for solutions of the Stefan problem,”Dokl. Akad. Nauk Ukr. SSR, 4–6 (1981).
[12]
S. V. Saley, “On the velocity of convergence of the free boundary to the limit position in a Stefan problem,”Dokl Akad. Nauk Ukr. SSR, 19–23 (1981).
[13]
E. I. Kim and G. I. Bizhanova, “Investigation of the second boundary Stefan problem for small time,”Vestn. Akad. Nauk Kazakh. SSR, 76–86 (1981).
[14]
E. I. Kim and G. I. Bizhanova, “On a class of integrodifferential equations,”Vestn. Akad. Nauk Kazakh. SSR, 38–48 (1982).
[15]
V. A. Florin, “Condensation of a soil-medium and filtration with varying porosity taking account of connected water influence,”Izv. Akad. Nauk SSR, Otdel. Tekh. Nauk, 1635–1649 (1951).
[16]
T. D. Ventsel, “A problem for the heat equation with a free boundary,”Dokl. Akad. Nauk SSSR,131, 1000–1003 (1960).
[17]
Nguen Din Chi, “A problem for a parabolic equation with free boundary,”Vestn. Moskov. Univ., 40–54 (1966); 51–62 (1966).
[18]
D. M. Syons and R. H. Martin, “A moving boundary problem modelling diffusion with nonlinear absorption,”J. Differ. Equat.,51, 267–294 (1984). 10.1016/0022-0396(84)90111-6
[19]
I. V. Bocharova, “Asymptotic behavior of solutions of a free boundary problem for the heat equation,”Dokl. Akad. Nauk SSSR,143, 259–261 (1962).
[20]
N. N. Verigin, “Pressing of viscous solutions in grounds for strengthening and water unpermeation of bases of hydrotechnical constructions,”Izv. Akad. Nauk SSSR, Otdel. Tekh. Nauk, 674–687 (1952).
[21]
A. I. Tikhonov and A. A. Samarskii,Equations of Mathematical Physics [in Russian], Moscow (1972).
[22]
M. Muskat,The Flow of Homogeneous Fluids through Porous Media, Michigan (1946).
[23]
L. I. Rubinshtein, “On a solution of N. N. Verigin’s problem,”Dok. Akad. Nauk SSSR,113, 50–53 (1957).
[24]
L. I. Kamynin, “On the existence of a solution of the Verigin problem,”J. Comput. Math. Phys.,2, 833–858 (1962).
[25]
L. I. Kamynin, “On a linear Verigin problem,”Dokl. Akad. Nauk SSSR,150, 1210–1213 (1963).
[26]
A free boundary problem and an extension of Muskat's model

W. Fulks, R. B. Guenther

Acta Mathematica 1969 10.1007/bf02392014
[27]
A. Begmatov, “On asymptotic solutions of certain plane filtration and diffusion free boundary problems,” in:Boundary-Value Problems for Differential Equations (1973), pp. 135–144.
[28]

Lawrence Evans

Indiana University Mathematics Journal 1977 10.1512/iumj.1977.26.26074
[29]
L. S. Evans and A. Friedman, “Regularity and asymptotic behavior of two immiscible fluids in a one-dimensional porous medium,”J. Differ. Equat.,31, 366–391 (1979). 10.1016/s0022-0396(79)80007-8
[30]
I. Pavlov, “On a free boundary problem for parabolic equations,”Contr. Cybern.,7, 19–37 (1978).
[31]
A. M. Meirmanov, “On the solvability of the Verigin problem in an exact formulation,”Dokl. Akad. Nauk SSSR,253, 588–591 (1980).
[32]
L. Jin, “The one-dimensional Verigin problem,”J. Part. Differ. Equat.,4, 74–96 (1991).
[33]
V. S. Belonosov and T. I. Zelenyak,Nonlocal Problems in the Theory of Quasilinear Parabolic Equations [in Russian], Novosibirsk (1975).
[34]
V. S. Belonosov, “Estimates of solutions of parabolic systems in weighted Hölder classes and some of their applications,”Mat. Sb.,110, 163–188 (1979).
[35]
V. A. Solonnikov, “On an estimate of the maximum modulus of derivatives of a solution of a homogeneous parabolic initial-boundary value problem,” Preprint LOMI, P-2-77 (1977).
[36]
V. A. Solonnikov and A. G. Khachatryan, “Estimates of solutions of parabolic initial-boundary value problems in Hölder norms,”Tr. Mat. Inst. Akad. Nauk SSSR,147, 147–155 (1980).
[37]
G. I. Bizhanova and V. A. Solonnikov, “Solvability of an initial-boundary value problem with time derivative in the boundary condition for a second-order parabolic equation in a weighted Hölder function space,”Algebra Analiz,5, 99–134 (1993).
[38]
E. V. Domanova, “Estimates for solutions of parabolic systems in weighted Hölder classes without compatibility conditions,” in:Embedding Theorems and Their Application to Problems of Mathematical Physics (1989), pp. 70–85.
[39]
G. I. Bizhanova, “Solution of an initial-boundary value problem with time derivative in the conjugation condition for a second-order parabolic equation in a weighted Hölder space,”Algebra Analiz,6, 62–92. (1994).
[40]
G. I. Bizhanova, “Investigation of solvability of the multidimensional two-phase Stefan problems and the Florin problem on nonstationary filtration for second-order parabolic equations in a weighted Hölder function space (the Cauchy-Stefan and Cauchy-Florin problems),”Zap. Nauchn. Semin. POMI,213, 14–47 (1994).
[41]
G. I. Bizhanova, “Solution in a weighted Hölder function space of the multidimensional two-phase Stefan and Florin problems for a second-order parabolic equation in a bounded domain,”Algebra Analiz 7, 46–76 (1995).
[42]
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva,Linear and Quasilinear Equations of Parabolic Type [in Russian], Moscow (1967). 10.1090/mmono/023
[43]
G. I. Bizhanova, “Estimates of solutions ofn-dimensional conjugation problem for the heat equation in weighted Hölder norms, I. II,”Izv. Akad. Nauk Resp. Kazakh., 7–13 (1992); 11–17 (1993).
[44]
G. Bateman and A. Erdelyi,Tables of Integral Transforms [Russian translation], Moscow (1969).
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Published
Mar 01, 2000
Vol/Issue
99(1)
Pages
816-836
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G. I. Bizhanova (2000). Classical solvability for one-dimensional, free boundary, Florin, Muskat-Verigin, and Stefan problems. Journal of Mathematical Sciences, 99(1), 816-836. https://doi.org/10.1007/bf02673591