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.

**[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