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Book Review

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Book Information:

Author: Morton E. \linebreak Gurtin
Title: Thermomechanics of evolving phase boundaries in the plane
Additional book information: Oxford University Press, Oxford and New York, 1993, xi+148 pp., US$54.00. ISBN 019-853694-1.

References [Enhancements On Off] (What's this?)

  • [1] U. Abresch and J. S. Langer, The normalized curve shortening flow and homothetic solutions, J. Differential Geom. 23 (1986), 175-196. MR 845704 (88d:53001)
  • [2] F. J. Almgren, Jr., and L. Wang, Mathematical existence of crystal growth with Gibbs-Thomson curvature effects, Preprint, 1994.
  • [3] J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. 1. Interfacial free energy, J. Chem. Phys. 28 (1958), 358-367.
  • [4] S. J. Chapman, S. D. Howison, and J. R. Ockendon, Macroscopic models for superconductivity, SIAM Rev. 34 (1992), 529-560. MR 1193011 (94b:82037)
  • [5] B. Derrida, J. L. Lebowitz, E. R. Speer, and H. Spohn, Dynamics of an anchored Toom interface, J. Phys. A 24 (1991), 4805-4834. MR 1131256 (92g:82079)
  • [6] R. Dobrushin, R. Kotecky, and S. Shlosman, Wulff construction: A global shape from local interaction, Transl. Math. Monographs., vol. 104, Amer. Math. Soc., Providence, RI, 1992. MR 1181197 (93k:82002)
  • [7] L. C. Evans and J. Spruck, Motion of level sets by mean curvature. 1, J. Differential Geom. 33 (1991), 635-681. MR 1100206 (92h:35097)
  • [8] G. J. Fix, Numerical simulation of free boundary problems using phase field methods, The Mathematics of Finite Elements and Applications IV (Uxbridge, 1981), Academic Press, London and New York, 1982, p. 265.
  • [9] M. Gage and R. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom. 23 (1986), 69-96. MR 840401 (87m:53003)
  • [10] M. A. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom. 26 (1987), 285-314. MR 906392 (89b:53005)
  • [11] W. Kurz and D. J. Fisher, Fundamentals of solidification, third ed., Trans Tech Publications, Aedermannsdorf, Switzerland, 1989.
  • [12] S. Luckhaus, Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature, European J. Appl. Math. 1 (1990), 101-111. MR 1117346 (92i:80004)
  • [13] W. W. Mullins, Two-dimensional motion of idealized grain boundaries, J. Appl. Phys. 27 (1956), 900-904. MR 0078836 (17:1252g)
  • [14] O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Phys. D 43 (1990), 44-62. MR 1060043 (91h:82034)
  • [15] J. A. Sethian and J. Strain, Crystal growth and dendritic solidification, J. Comput. Phys. 98 (1992), 231-253. MR 1150905 (92k:80002)
  • [16] W. A. Tiller, The science of crystallization: Macroscopic phenomena and defect generation, Cambridge Univ. Press, Cambridge and New York, 1991.
  • [17] A. A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phase-field model for isothermal phase transitions in binary alloys, Phys. Rev. A 45(10) (1992), 7424-7439.

Review Information:

Reviewer: John Strain
Journal: Bull. Amer. Math. Soc. 32 (1995), 431-434
DOI: https://doi.org/10.1090/S0273-0979-1995-00611-7
American Mathematical Society