On the structure of equilibrium phase transitions within the gradient theory of fluids
Authors:
Morton E. Gurtin and Hiroshi Matano
Journal:
Quart. Appl. Math. 46 (1988), 301-317
MSC:
Primary 49B21; Secondary 73G10, 76A02, 80A20
DOI:
https://doi.org/10.1090/qam/950604
MathSciNet review:
950604
Full-text PDF Free Access
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Additional Information
- Shmuel Agmon, Lectures on elliptic boundary value problems, Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. MR 0178246
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J. W. Cahn, On spinodal decomposition, Acta Met. 9, 795–801 (1961)
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28, 258–267 (1958)
J. W. Cahn and J. E. Hilliard, Spinodal decomposition: a reprise, Acta Met. 19, 151–161 (1971)
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J. D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density (in Dutch), Verh. Konink. Akad. Wetensch. Amsterdam (Sect. 1) Vol. 1, No. 8 (1893)
S. Agmon, Lectures on elliptic boundary value problems, Van Nostrand Math. Studies 2, Princeton, 1965
C. Bandle, Isoperimetric inequalities and applications, Pitman, Boston, 1980
J. W. Cahn, On spinodal decomposition, Acta Met. 9, 795–801 (1961)
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28, 258–267 (1958)
J. W. Cahn and J. E. Hilliard, Spinodal decomposition: a reprise, Acta Met. 19, 151–161 (1971)
A. P. Calderon, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80, 16–36 (1958)
J. Carr, M. E. Gurtin, and M. Slemrod, Structured phase transitions on a finite interval, Arch. Rat. Mech. Anal. 86, 317–351 (1984)
R. G. Casten and C. J. Holland, Instability results for reaction diffusion equations with Neumann boundary conditions, J. Differential Equations 27, 266–273 (1978)
N. Chafee, Asymptotic behavior for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions, J. Differential Equations 18, 111–134 (1975)
E. Conway, D. Hoff, and J. Smoller, Large time behavior of systems of nonlinear reaction-diffusion equations, SIAM J. Appl. Math. 35, 1–16 (1978)
P. Grisvard, Elliptic problems in nonsmooth domains, Pitman, Boston, 1984
P. Hartman and A. Wintner, On the local behavior of solutions of non-parabolic partial differential equations, Amer. J. Math. 75, 449–476 (1953)
S. Jimbo, Singular perturbations of domains and semilinear elliptic equations, J. Fac. Sci. Univ. Tokyo. To appear.
B. Kawohl, Rearrangements and convexity of level sets in PDE, Lecture Notes in Math. 1150, Springer-Verlag, Berlin, 1985
B. Kawohl, On the isoperimetric nature of a rearrangement inequality and its consequences for some variational problems, Arch. Rat. Mech. Anal. 94, 227–243 (1986)
H. Matano, Asymptotic behavior and stability of solutions of semilinear diffusion equations, Publ. Res. Inst. Math. Sci. 15, 401–454 (1979)
H. Matano, Nonincrease of the lap-number of a solution for a one-dimensional parabolic equation, J. Fac. Sci. Univ. Tokyo Sec. IA 29, 401–441 (1982)
L. E. Payne and H. F. Weinberger, An optimal Poincaré inequality for convex domains, Arch. Rat. Mech. Anal. 5, 286–292 (1960)
J. S. Rowlinson, Translation of J. D. van der Waals’ “The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density,” J. Statist. Phys. 20, 197–244 (1979)
J. D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density (in Dutch), Verh. Konink. Akad. Wetensch. Amsterdam (Sect. 1) Vol. 1, No. 8 (1893)
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Article copyright:
© Copyright 1988
American Mathematical Society