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Book Review
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Book Information
Author(s):
Morton E. 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:
- [1]
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- [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. {\rm 1.} {Interfacial} free energy, J. Chem. Phys. \textbf{28} (1958), 358--367.
- [4]
- S.~J. Chapman, S.~D. Howison, and J.~R. Ockendon, Macroscopic models for superconductivity, SIAM Rev. \textbf{34} (1992), 529--560.
- [5]
- B.~Derrida, J.~L. Lebowitz, E.~R. Speer, and H.~Spohn, Dynamics of an anchored {Toom} interface, J. Phys. A \textbf{24} (1991), 4805--4834.
- [6]
- R.~Dobrushin, R.~Kotecky, and S.~Shlosman, \emph{Wulff construction\/\RM : A global shape from local interaction}, Amer. Math. Soc., Providence, RI, 1992.
- [7]
- L.~C. Evans and J.~Spruck, Motion of level sets by mean curvature. \RM 1, J. Differential Geom. \textbf{33} (1991), 635--681.
- [8]
- G.~J. Fix, \emph{Numerical simulation of free boundary problems using phase field methods}, Academic Press, London and New York, 1982.
- [9]
- M.~Gage and R.~Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom. \textbf{23} (1986), 69--96.
- [10]
- M.~A. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom. \textbf{26} (1987), 285--314.
- [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. \textbf{1} (1990), 101--111.
- [13]
- W.~W. Mullins, Two-dimensional motion of idealized grain boundaries, J. Appl. Phys. \textbf{27} (1956), 900--904.
- [14]
- O.~Penrose and P.~C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Phys. D \textbf{43} (1990), 44--62.
- [15]
- J.~A. Sethian and J.~Strain, Crystal growth and dendritic solidification, J. Comput. Phys. \textbf{98} (1992), 231--253.
- [16]
- W.~A. Tiller, The science of crystallization\/\RM : 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 \textbf{45(10)} (1992), 7424--7439.
Additional Information:
Reviewer(s):
John
Strain
Review Information:
Journal:
Bull. Amer. Math. Soc.
32
(1995),
431-434.
DOI:
10.1090/S0273-0979-1995-00611-7
PII:
S 0273-0979(1995)00611-7
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