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Online ISSN 1552-4485; Print ISSN 0033-569X
On a nonequilibrium thermodynamics of capillarity and phase
Author:
Morton E. Gurtin
Journal:
Quart. Appl. Math. 47 (1989), 129-145
MSC:
Primary 80A15; Secondary 35K55, 76R50
DOI:
https://doi.org/10.1090/qam/987902
MathSciNet review:
987902
Full-text PDF Free Access
References | Similar Articles | Additional Information
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J. W. Gibbs, On the equilibrium of heterogeneous substances, Trans. Connecticut Acad. 3, 108–248 (1876), 343–524 (1878). Reprinted in: The Scientific Papers of J. Willard Gibbs, Vol. 1, Dover, New York, 1961
J. D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density (in Dutch), Verhandel. Konink. Akad. Weten. Amsterdam (Sec. 1) Vol. 1, No. 8 (1893)
D. J. Korteweg, Sur la forme que prennent les équations des mouvement des fluides si l’on tientcomple des forces capillaires par des variations de densité, Arch. Neerl. Sci. Exactes Nat. Ser. 11, 6, 1–24 (1901)
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28, 258–267 (1958)
L. D. Landau and E. M. Lifschitz, Electrodynamics of Continuous Bodies, Pergamon, New York, 1960
- Bernard D. Coleman and Walter Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13 (1963), 167–178. MR 153153, DOI https://doi.org/10.1007/BF01262690 J. W. Cahn, On spinodal decomposition, Acta Metallurgica 9, 795–801 (1961) J. W. Cahn, On spinodal decomposition in cubic crystals, Acta Metallurgica 10, 179–183 (1962) J. W. Cahn and J. E. Hilliard, Spinodal decomposition: a reprise, Acta Metallurgica 19, 151–161 (1971) D. W. Hoffman and J. W. Cahn, A vector thermodynamics for anisotropic surfaces-1. Fundamentals and applications to plane surface junctions, Surface Sci. 31, 368–388 (1972) J. W. Cahn and D. W. Hoffman, A vector thermodynamics for anisotropic surfaces-2. Curved and faceted surfaces, Acta Metallurgica 22, 1205–1214 (1974) B. Widom, Structure and thermodynamics of interfaces, in Statistical Mechanics and Statistical Methods in Theory and Application, Plenum, New York, 1977
- J. Fernandez-Diaz and W. O. Williams, A generalized Stefan condition, Z. Angew. Math. Phys. 30 (1979), no. 5, 749–755 (English, with German summary). MR 553277, DOI https://doi.org/10.1007/BF01590684
- Morton E. Gurtin, Toward a nonequilibrium thermodynamics of two-phase materials, Arch. Rational Mech. Anal. 100 (1988), no. 3, 275–312. MR 918798, DOI https://doi.org/10.1007/BF00251518
- J. E. Dunn and J. Serrin, On the thermomechanics of interstitial working, Arch. Rational Mech. Anal. 88 (1985), no. 2, 95–133. MR 775366, DOI https://doi.org/10.1007/BF00250907
- Basil Nicolaenko and Bruno Scheurer, Low-dimensional behavior of the pattern formation Cahn-Hilliard equation, Trends in the theory and practice of nonlinear analysis (Arlington, Tex., 1984) North-Holland Math. Stud., vol. 110, North-Holland, Amsterdam, 1985, pp. 323–336. MR 817507, DOI https://doi.org/10.1016/S0304-0208%2808%2972727-0
- Amy Novick-Cohen, Energy methods for the Cahn-Hilliard equation, Quart. Appl. Math. 46 (1988), no. 4, 681–690. MR 973383, DOI https://doi.org/10.1090/S0033-569X-1988-0973383-6 J. A. Serrin, Continuum model for chemical mixture dynamics, Developments in Mechanics 13, Appl. Mech. Div., Am. Soc. Mech. Eng., 1985
- Wolf von Wahl, On the Cahn-Hilliard equation $u’+\Delta ^2u-\Delta f(u)=0$, Delft Progr. Rep. 10 (1985), no. 4, 291–310. Mathematics and mathematical engineering (Delft, 1985). MR 839466
- Charles M. Elliott and Zheng Songmu, On the Cahn-Hilliard equation, Arch. Rational Mech. Anal. 96 (1986), no. 4, 339–357. MR 855754, DOI https://doi.org/10.1007/BF00251803
- Morton E. Gurtin, On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96 (1986), no. 3, 199–241. MR 855304, DOI https://doi.org/10.1007/BF00251907
- Amy Novick-Cohen and Lee A. Segel, Nonlinear aspects of the Cahn-Hilliard equation, Phys. D 10 (1984), no. 3, 277–298. MR 763473, DOI https://doi.org/10.1016/0167-2789%2884%2990180-5
- Zheng Songmu, Asymptotic behavior of solution to the Cahn-Hillard equation, Appl. Anal. 23 (1986), no. 3, 165–184. MR 870486, DOI https://doi.org/10.1080/00036818608839639
- Charles M. Elliott and Donald A. French, Numerical studies of the Cahn-Hilliard equation for phase separation, IMA J. Appl. Math. 38 (1987), no. 2, 97–128. MR 983721, DOI https://doi.org/10.1093/imamat/38.2.97
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Article copyright:
© Copyright 1989
American Mathematical Society