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Modified Stefan problem, regularization problem, and interior layers

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Abstract

The paper considers the problem of justifying the asymptotic solution of the phase-field system.

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REFERENCES

  1. M. S. Berger L. E. Fraenkel (1970) ArticleTitleOn the asymptotic solution of a nonlinear Dirichlet problem J. Math. Mech. 19 553–585

    Google Scholar 

  2. G. Caginalp (1986) ArticleTitleAn analysis of a phase field model of a free boundary Arch. Mech. Anal. 92 205–245

    Google Scholar 

  3. X. Chen (1994) ArticleTitleSpectrum for the Allen-Cahn, Cahn-Hilliard, and phase-field equations for general interfaces Comm. Part. Differ. Equat. 19 IssueID7 1371–1395

    Google Scholar 

  4. V. G. Danilov G. A. Omel’yanov E. V. Radkevich (1995) ArticleTitleAsymptotic solution of the phase-field system and the modified Stefan problem Differents. Uravn. 31 IssueID3 483–491

    Google Scholar 

  5. V. G. Danilov, G. A. Omel’yanov, and E. V. Radkevich, “Hugoniot-type conditions and weak solutions to the phase field system,” Eur. J. Appl. Math.(1999).

  6. O. Oleinik M. Primicerio E. Radkevich (1993) ArticleTitleStefan-like problems Meccanica 28 129–143

    Google Scholar 

  7. E. Radkevich, “On the conditions for existence of the classical solution to the modified Stefan problem (the Gibbs-Thompson law),” Mat. Sb., 183 No.2 (1992).

    Google Scholar 

  8. E. V. Radkevich (1993) ArticleTitleAsymptotic solutions of the phase-field system Differents. Uravn. 29 IssueID3 487–500

    Google Scholar 

  9. E. Radkevich, “Well-posedness of models of continuum mechanics and thermodynamics,” in this issue.

  10. O. Vasil’eva E. Radkevich D. Hilhorst (2000) ArticleTitleThe classical Verigin-Masket problem, the regularization problem, and the interior layers Trudy Mosk. Mat. Obsch. 61 25–74

    Google Scholar 

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Authors
  1. O. A. Vasil’eva
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Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 3, Partial Differential Equations, 2003.

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Vasil’eva, O.A. Modified Stefan problem, regularization problem, and interior layers. J Math Sci 125, 405–418 (2005). https://doi.org/10.1007/s10958-005-0002-9

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