Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Traveling wave solutions for interfaces arising from phase boundaries based on a phase field model

Author: J. W. Wilder
Journal: Quart. Appl. Math. 49 (1991), 333-350
MSC: Primary 80A22
DOI: https://doi.org/10.1090/qam/1106396
MathSciNet review: MR1106396
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Abstract: This work presents an analysis of the traveling wave solutions resulting from the phase field model which has been proposed for solidification. It is shown that solutions only exist for very restricted values of the parameters involved and these values are investigated. The basic nature of the traveling wave solutions resulting from this model are also discussed.

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  • [1] G. Caginalp, Surface tension and supercooling in solidification theory, (Proc. Sitges conference on statistical mechanics, Sitges, 1984) ed. by L. Garrido, Lecture Notes in Physics, Vol. 216, Springer, New York, 1984
  • [2] Gunduz Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal. 92 (1986), no. 3, 205–245. MR 816623, https://doi.org/10.1007/BF00254827
  • [3] G. Caginalp and P. C. Fife, Phase field methods for interfacial boundaries, Phys. Rev. B. 33, 7792-7794 (1986)
  • [4] G. Caginalp and P. C. Fife, Higher-order phase field models and detailed anisotropy, Phys. Rev. B. 34, 4940-4943
  • [5] G. Caginalp and P. C. Fife, Qualitative properites of solutions, Non-Linear Parabolic equations, Pitman, Boston, 1987
  • [6] G. Caginalp and P. C. Fife, Dynamics of layered interfaces arising from phase boundaries, SIAM J. Appl. Math. 48 (1988), no. 3, 506–518. MR 941098, https://doi.org/10.1137/0148029
  • [7] Gunduz Caginalp and Bryce McLeod, The interior transition layer for an ordinary differential equation arising from solidification theory, Quart. Appl. Math. 44 (1986), no. 1, 155–168. MR 840451
  • [8] J. T. Lin, The numerical analysis of a phase field model in moving boundary problems, SIAM J. Numer. Anal. 25 (1988), no. 5, 1015–1031. MR 960863, https://doi.org/10.1137/0725058
  • [9] L. I. Rubenšteĭn, The Stefan problem, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by A. D. Solomon; Translations of Mathematical Monographs, Vol. 27. MR 0351348
  • [10] G. Caginalp, Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations, Phys. Rev. A (3) 39 (1989), no. 11, 5887–5896. MR 998924, https://doi.org/10.1103/PhysRevA.39.5887
  • [11] J. W. Wilder, An Asymptotic Solution to the Stefan Problem Near the Interface, unpublished work

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DOI: https://doi.org/10.1090/qam/1106396
Article copyright: © Copyright 1991 American Mathematical Society

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