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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G. Caginalp and P. C. Fife, Higher-order phase field models and detailed anisotropy, Phys. Rev. B. 34, 4940–4943
G. Caginalp and P. C. Fife, Qualitative properites of solutions, Non-Linear Parabolic equations, Pitman, Boston, 1987
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J. W. Wilder, An Asymptotic Solution to the Stefan Problem Near the Interface, unpublished work
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
G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal. 92, 205–245 (1986)
G. Caginalp and P. C. Fife, Phase field methods for interfacial boundaries, Phys. Rev. B. 33, 7792–7794 (1986)
G. Caginalp and P. C. Fife, Higher-order phase field models and detailed anisotropy, Phys. Rev. B. 34, 4940–4943
G. Caginalp and P. C. Fife, Qualitative properites of solutions, Non-Linear Parabolic equations, Pitman, Boston, 1987
G. Caginalp and P. C. Fife, Dynamics of layered interfaces arising from phase boundaries, SIAM J. Appl. Math. 48 506–157 (1988)
G. Caginalp and B. McLeod, The internal transition layer for an ordinary differential equation arising from solidification theory, Quart. Appl. Math. 44, 155–168 (1986)
J. T. Lin, The numerical analysis of a phase field model in moving boundary problems, SIAM J. Numer. Anal. 25, 1015–1031 (1988)
L. I. Rubinstein, The Stefan Problem, Amer. Math. Soc. Transl., vol. 27, Amer. Math. Soc., Providence, RI, 1971
G. Caginalp, Stefan and Hele Shaw Type Models as Asymptotic Limits of the Phase Field Model, in press
J. W. Wilder, An Asymptotic Solution to the Stefan Problem Near the Interface, unpublished work
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Article copyright:
© Copyright 1991
American Mathematical Society
