no. 3
Some models of Cahn-Hilliard equations in nonisotropic media
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 3, pp. 539-554. 
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     author = {Miranville, Alain},
     title = {Some models of {Cahn-Hilliard} equations in nonisotropic media},
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     pages = {539--554},
     publisher = {Dunod},
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     volume = {34},
     number = {3},
     year = {2000},
     mrnumber = {1763524},
     zbl = {0965.35170},
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     url = {http://www.numdam.org/item/M2AN_2000__34_3_539_0/}
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Miranville, Alain. Some models of Cahn-Hilliard equations in nonisotropic media. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 3, pp. 539-554. http://www.numdam.org/item/M2AN_2000__34_3_539_0/

[1] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of partial differential equations satisfying general boundary conditions I, II, Comm. Pure Appl. Math. 12 (1959) 623-727 ; 17 (1964) 35-92. | Zbl

[2] A. Babin and B. Nicolaenko, Exponential attractors of reaction-diffusion Systems in an unbounded domain. J. Dyn. Differential Equations 7 (1995) 567-590. | MR | Zbl

[3] A. V. Babin and M. I. Vishik, Attractors of evolution equations. North-Holland, Amsterdam (1991). | MR | Zbl

[4] H. Brezis, Analyse fonctionnelle, théorie et applications. Masson (1983). | MR | Zbl

[5] J. W. Cahn, On spinodal decomposition. Acta Metall. 9 (1961) 795-801.

[6] J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform System I. Interfacial free energy. J. Chem. Phys. 2 (1958) 258-267.

[7] M. Carrive, A. Miranville, A. Piétrus and J. M. Rakotoson, The Cahn-Hilliard equation for an isotropic deformable continuum. Appl. Math. Letters 12 (1999) 23-28. | MR | Zbl

[8] M. Carrive, A. Miranville and A. Piétrus, The Cahn-Hilliard equation for deformable elastic continua. Adv. Math. Sci. Appl. (to appear). | MR | Zbl

[9] V. V. Chepyzhov and M. I. Vishik, Attractors of nonautonomous dynamical systems and their dimension. J. Math. Pures Appl. 73 (1994) 279-333. | MR | Zbl

[10] L. Cherfils and A. Miranville, Generalized Cahn-Hilliard equations with a logarithmic free energy (submitted). | Zbl

[11] J. W. Cholewe and T. Dlotko, Global attractors of the Cahn-Hilliard system. Bull. Austral. Math. Soc. 49 (1994) 277-302. | MR | Zbl

[12] A. Debussche and L. Dettori, On the Cahn-Hilliard equation with a logarithmic free energy. Nonlinear Anal. TMA 24 (1995) 1491-1514. | MR | Zbl

[13] A. Eden, C. Foias, B. Nicolaenko and R. Temam, Exponential attractors for dissipative evolution equations. Masson (1994). | MR | Zbl

[14] M. Efendiev and A. Miranville, Finite dimensional attractors for a class of reaction-diffusion equations in Rn with a strong nonlinearity. Disc. Cont. Dyn. Systems 5 (1999) 399-424. | MR | Zbl

[15] C. M. Elliot and S. Luckhauss, A generalized equation for phase separation of a multi-component mixture with interfacial free energy. Preprint.

[16] P. Fabrie and A. Miranville, Exponential attractors for nonautonomous first-order evolution equations. Disc. Cont. Dyn. Systems 4 (1998) 225-240. | MR | Zbl

[17] C. Galusinski, Perturbations singulières de problèmes dissipatifs : étude dynamique via l'existence et la continuité d'attracteurs exponentiels. Thèse, Université Bordeaux-I (1996).

[18] C. Galusinski, M. Hnid and A. Miranville, Exponential attractors for nonautonomous partially dissipative equations. Differential Integral Equations 12 (1999) 1-22. | MR | Zbl

[19] M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Physica D 92 (1996) 178-192. | MR | Zbl

[20] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969). | MR | Zbl

[21] D. Li and C. Zhong, Global attractor for the Cahn-Hilliard system with fast growing nonlinearity. J. Differential Equations (1998) | MR | Zbl

[22] M. Marion and R. Temam, Navier-Stokes equations, theory and approximation, in Handbook of numerical analysis, P. G. Ciarlet and J. L. Lions eds. (to appear) | MR | Zbl

[23] A. Miranville, Exponential attractors for nonautonomous evolution equations. Appl. Math. Letters 11 (1998) 19-22. | MR

[24] A. Miranville, Exponential attractors for a class of evolution equations by a decomposition method. C. R. Acad. Sci. 328 (1999) 145-150. | MR | Zbl

[25] A. Miranville, Long time behavior of some models of Cahn-Hilliard equations in deformable continua. Nonlinear Anal. Series B (to appear). | MR | Zbl

[26] A. Miranville, Exponential attractors for a class of evolution equations by a decomposition method. II. The nonautonomous case C. R. Acad. Sci. 328 (1999) 907-912. | MR | Zbl

[27] A. Miranville, Equations de Cahn-Hilliard généralisées dans un milieu déformable. C. R. Acad. Sci. 328 (1999) 1095-1100. | MR | Zbl

[28] A. Miranville, A model of Cahn-Hilliard equation based on a microforce balance. C. R. Acad. Sci. 328 (1999) 1247-1252. | MR | Zbl

[29] A. Miranville, A. Piétrus and J. M. Rakotoson, Dynamical aspect of a generalized Cahn-Hilliard equation based on a microforce balance. Asymptotic Anal. 16 (1998) 315-345. | MR | Zbl

[30] B. Nicolaenko, B. Scheurer and R. Temam, Some global dynamical properties of a class of pattern formation equations. Comm. Partial Differential Equations 14 (1989) 245-297. | MR | Zbl

[31] R. Temam, Infinite dimensional dynamical systems in mechanics and physics. 2nd. ed., Springer-Verlag, New-York (1997). | MR | Zbl