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Mat. Sb., 1992, Volume 183, Number 2, Pages 77–101 (Mi msb1468)  

This article is cited in 31 scientific papers (total in 31 papers)

On conditions for the existence of a classical solution of the modified Stefan problem (the Gibbs–Thomson law)

E. V. Radkevich

Abstract: Sufficient conditions close to necessary are obtained for the existence of a solution (unique for $\sigma>0$ and $\beta>0$) of a solution of the modified Stefan problem on a small time interval.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1993, 75:1, 221–246

Bibliographic databases:

MSC: Primary 35K15, 80A22; Secondary 35R35
Received: 27.02.1991

Citation: E. V. Radkevich, “On conditions for the existence of a classical solution of the modified Stefan problem (the Gibbs–Thomson law)”, Mat. Sb., 183:2 (1992), 77–101; Russian Acad. Sci. Sb. Math., 75:1 (1993), 221–246

Citation in format AMSBIB
\by E.~V.~Radkevich
\paper On conditions for the existence of a~classical solution of the modified Stefan problem (the Gibbs--Thomson law)
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 2
\pages 77--101
\jour Russian Acad. Sci. Sb. Math.
\yr 1993
\vol 75
\issue 1
\pages 221--246

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    This publication is cited in the following articles:
    1. Radkevich E., Eshonkulov B., “On the Existence of the Classical Solution of the Glassy Polymer Impregnation Problem”, Dokl. Akad. Nauk, 325:4 (1992), 668–673  mathnet  mathscinet  zmath  isi
    2. E. V. Radkevich, “On the spectrum of the pencil in the Verigin–Muskat problem”, Russian Acad. Sci. Sb. Math., 80:1 (1995), 33–73  mathnet  crossref  mathscinet  zmath  isi
    3. Radkevich E., “On the Asymptotic Solutions of a Phase Field System”, Differ. Equ., 29:3 (1993), 418–429  mathnet  mathscinet  zmath  isi
    4. Radkevich E., “The Heat Stefan Wave”, Dokl. Akad. Nauk, 328:6 (1993), 657–661  mathnet  zmath  isi
    5. E. V. Radkevich, B. O. Ètonkulov, “On the existence of classical solutions of the problem on swelling of glassy polymers”, Math. Notes, 57:6 (1995), 615–624  mathnet  crossref  mathscinet  zmath  isi
    6. V. G. Danilov, G. A. Omel'yanov, E. V. Radkevich, “Justification of asymptotics of solutions of the phase-field equations and a modified Stefan problem”, Sb. Math., 186:12 (1995), 1753–1771  mathnet  crossref  mathscinet  zmath  isi
    7. Danilov V., Omelyanov G., Radkevich E., “The Modified Stefan Problem as a Limit of Asymptotic Solution for Phase Field System”, Dokl. Akad. Nauk, 343:5 (1995), 586–589  mathnet  mathscinet  zmath  isi
    8. Danilov V., Omelyanov G., Radkevich E., “Asymptotics of the Solution to the Phase Field System and the Modified Stefan Problem”, Differ. Equ., 31:3 (1995), 446–454  mathnet  mathscinet  zmath  isi
    9. Fahuai Yi, “A note on the classical solution of a two-dimensional superconductor free boundary problem”, Eur J Appl Math, 7:2 (1996)  crossref  mathscinet  zmath
    10. Yi F., “Classical Solution of Quasi-Stationary Stefan Problem”, Chin. Ann. Math. Ser. B, 17:2 (1996), 175–186  mathscinet  zmath  isi
    11. Chen X., Hong J., Yi F., “Existence, Uniqueness, and Regularity of Classical Solutions of the Mullins-Sekerka Problem”, Commun. Partial Differ. Equ., 21:11-12 (1996), 1705–1727  mathscinet  zmath  isi
    12. Tao Y., “Classical Solution of Verigin Problem with Surface Tension”, Chin. Ann. Math. Ser. B, 18:3 (1997), 393–404  mathscinet  zmath  isi
    13. Omelyanov G., Radkevich E., Danilov V., “The Problem of the Phase Transition in the Phase Field System”, Dokl. Akad. Nauk, 352:6 (1997), 731–734  mathnet  mathscinet  isi
    14. Yi F., “Asymptotic Behaviour of the Solutions of the Supercooled Stefan Problem”, Proc. R. Soc. Edinb. Sect. A-Math., 127:Part 1 (1997), 181–190  crossref  mathscinet  zmath  isi
    15. Yi Fahuai, “A free boundary problem of type-I superconductivity”, Acta Mathematicae Applicatae Sinica English Series, 14:1 (1998), 48  crossref  mathscinet  zmath
    16. Omel'yanov G. Danilov V. Radkevich E., “Asymptotic Solution of the Conserved Phase Field System in the Fast Relaxation Case”, Eur. J. Appl. Math., 9:Part 1 (1998), 1–21  crossref  mathscinet  isi
    17. Yoshiaki Kusaka, Atusi Tani, “On the Classical Solvability of the Stefan Problem in a Viscous Incompressible Fluid Flow”, SIAM J Math Anal, 30:3 (1999), 584  crossref  mathscinet  zmath  isi
    18. Yi F., Liu J., “Vanishing Specific Heat for the Classical Solutions of a Multidimensional Stefan Problem with Kinetic Condition”, Q. Appl. Math., 57:4 (1999), 661–672  mathscinet  zmath  isi
    19. Rodrigues J. Solonnikov V. Yi F., “On a Parabolic System with Time Derivative in the Boundary Conditions and Related Free Boundary Problems”, Math. Ann., 315:1 (1999), 61–95  crossref  mathscinet  zmath  isi
    20. Yi F., “On a Three-Dimensional Free Boundary Problem in Superconductivity Involving Mean Curvature”, Proc. R. Soc. Edinb. Sect. A-Math., 131:Part 1 (2001), 205–224  crossref  mathscinet  zmath  isi
    21. Christof Eck, Peter Knabner, Sergey Korotov, “A Two-Scale Method for the Computation of Solid–Liquid Phase Transitions with Dendritic Microstructure”, Journal of Computational Physics, 178:1 (2002), 58  crossref  elib
    22. Fahuai Yi, Yuqing Liu, “Two-Phase Stefan Problem as the Limit Case of Two-Phase Stefan Problem with Kinetic Condition”, Journal of Differential Equations, 183:1 (2002), 189  crossref
    23. Schweizer B., “A Stable Time Discretization of the Stefan Problem with Surface Tension”, SIAM J. Numer. Anal., 40:3 (2002), 1184–1205  crossref  mathscinet  zmath  isi
    24. Fahuai Yi, “Global classical solution of Muskat free boundary problem”, Journal of Mathematical Analysis and Applications, 288:2 (2003), 442  crossref
    25. Solonnikov V., “Lectures on Evolution Free Boundary Problems: Classical Solutions”, Mathematical Aspects of Evolving Interfaces, Lecture Notes in Mathematics, 1812, ed. Ambrosio L. Mimura M. Deckelnick K. Solonnikov V. Dziuk G. Soner H. Colli P. Rodrigues J., Springer-Verlag Berlin, 2003, 123–175  crossref  mathscinet  zmath  isi
    26. Eck C., “Homogenization of a Phase Field Model for Binary Mixtures”, Multiscale Model. Simul., 3:1 (2005), 1–27  crossref  mathscinet  isi
    27. Pruess J., Simonett G., “Stability of Equilibria for the Stefan Problem with Surface Tension”, SIAM J. Math. Anal., 40:2 (2008), 675–698  crossref  mathscinet  zmath  isi
    28. V. I. Voititskiy, N. D. Kopachevskiy, P. A. Starkov, “Multicomponent conjugation problems and auxiliary abstract boundary-value problems”, Journal of Mathematical Sciences, 170:2 (2010), 131–172  mathnet  crossref  mathscinet
    29. Kopachevsky N.D., Voytitsky V.I., “On the Modified Spectral Stefan Problem and its Abstract Generalizations”, Modern Analysis and Applications: Mark Krein Centenary Conference, Vol 2, Operator Theory Advances and Applications, 191, eds. Adamyan V., Berezansky Y., Gohberg I., Gorbachuk M., Gorbachuk V., Kochubei A., Langer H., Popov G., Birkhauser Verlag Ag, 2009, 381–394  crossref  mathscinet  zmath  isi
    30. Ch. Eck, B. Jadamba, P. Knabner, “Error Estimates for a Finite Element Discretization of a Phase Field Model for Mixtures”, SIAM J Numer Anal, 47:6 (2010), 4429  crossref
    31. Pruess J. Simonett G. Zacher R., “Qualitative Behavior of Solutions for Thermodynamically Consistent Stefan Problems with Surface Tension”, Arch. Ration. Mech. Anal., 207:2 (2013), 611–667  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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