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A Cahn-Hilliard-Gurtin model with dynamic boundary conditions
1. | Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, United States |
2. | Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, 86962 Chasseneuil Futuroscope Cedex, France |
References:
[1] |
A. Bonfoh and A. Miranville, On Cahn-Hilliard-Gurtin equations, Nonlinear Anal., 47 (2001), 3455-3466. |
[2] |
J. W. Cahn, On spinodal decomposition, Acta Metall., 9 (1961), 795-801. |
[3] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system I. Interfacial free energy, J. Chem. Phys., 28 (1958), 258-267. |
[4] |
L. Cherfils, A. Miranville and S. Zelik, The Cahn-Hilliard equation with logarithmic potentials, Milan J. Math., 79 (2011), 561-596. |
[5] |
R. Chill, E. Fašangová and J. Prüss, Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions, Math. Nachr., 279 (2006), 1448-1462. |
[6] |
C. M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, in "Mathematical Models for Phase Change Problems" (ed. J. F. Rodrigues), International Series of Numerical Mathematics, Birkhäuser, Basel, 88 (1989). |
[7] |
H. P. Fischer, P. Maass and W. Dieterich, Novel surface modes in spinodal decomposition, Phys. Rev. Lett., 79 (1997), 893-896. |
[8] |
H. P. Fischer, P. Maass and W. Dieterich, Diverging time and length scales of spinodal decomposition modes in thin flows, Europhys. Lett., 42 (1998), 49-54.
doi: 10.2986/tren.001-0349. |
[9] |
H. P. Fischer, J. Reinhard, W. Dieterich, J.-F. Gouyet, P. Maass, A. Majhofer and D. Reinel, Time-dependent density functional theory and the kinetics of lattice gas systems in contact with a wall, J. Chem. Phys., 108 (1998), 3028-3037. |
[10] |
G. Gilardi, A. Miranville and G. Schimperna, On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions, Commun. Pure Appl. Anal., 8 (2009), 881-912. |
[11] |
G. Gilardi, A. Miranville and G. Schimperna, Long time behavior of the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions, Chinese Ann. Math., Ser. B, 31 (2010), 679-712. |
[12] |
M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192. |
[13] |
G. R. Goldstein, A. Miranville and G. Schimperna, A Cahn-Hilliard model in a domain with non-permeable walls, Physica D, 240 (2011), 754-766. |
[14] |
R. Kenzler, F. Eurich, P. Maass, B. Rinn, J. Schropp, E. Bohl and W. Dieterich, Phase separation in confined geometries: Solving the Cahn-Hilliard equation with generic boundary conditions, Comput. Phys. Commun., 133 (2001), 139-157. |
[15] |
A. Miranville, Some generalizations of the Cahn-Hilliard equation, Asymptotic Anal., 22 (2000), 235-259. |
[16] |
A. Miranville, Consistent models of Cahn-Hilliard-Gurtin equations with Neumann boundary conditions, Physica D, 158 (2001), 233-257. |
[17] |
A. Miranville, Generalized Cahn-Hilliard equations based on a microforce balance, J. Appl. Math., 2003 (2003), 165-185. |
[18] |
A. Miranville and S. Zelik, Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions, Math. Methods Appl. Sci., 28 (2005), 709-735. |
[19] |
A. Novick-Cohen, The Cahn-Hilliard equation: Mathematical and modeling perspectives, Adv. Math. Sci. Appl, 8 (1998), 965-985. |
[20] |
A. Novick-Cohen, The Cahn-Hilliard equation, in "Handbook of Differential Equations, Evolutionary Partial Differential Equations" (eds. C. M. Dafermos and M. Pokorny), 4, Elsevier, Amsterdam, (2008), 201-228. |
[21] |
J. Prüss, R. Racke and S. Zheng, Maximal regularity and asymptotic behavior of solutions for the Cahn-Hilliard equation with dynamic boundary conditions, Ann. Mat. Pura Appl. (4), 185 (2006), 627-648. |
[22] |
R. Racke and S. Zheng, The Cahn-Hilliard equation with dynamic boundary conditions, Adv. Diff. Eqns., 8 (2003), 83-110. |
[23] |
H. Wu and S. Zheng, Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions, J. Diff. Eqns., 204 (2004), 511-531. |
show all references
References:
[1] |
A. Bonfoh and A. Miranville, On Cahn-Hilliard-Gurtin equations, Nonlinear Anal., 47 (2001), 3455-3466. |
[2] |
J. W. Cahn, On spinodal decomposition, Acta Metall., 9 (1961), 795-801. |
[3] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system I. Interfacial free energy, J. Chem. Phys., 28 (1958), 258-267. |
[4] |
L. Cherfils, A. Miranville and S. Zelik, The Cahn-Hilliard equation with logarithmic potentials, Milan J. Math., 79 (2011), 561-596. |
[5] |
R. Chill, E. Fašangová and J. Prüss, Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions, Math. Nachr., 279 (2006), 1448-1462. |
[6] |
C. M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, in "Mathematical Models for Phase Change Problems" (ed. J. F. Rodrigues), International Series of Numerical Mathematics, Birkhäuser, Basel, 88 (1989). |
[7] |
H. P. Fischer, P. Maass and W. Dieterich, Novel surface modes in spinodal decomposition, Phys. Rev. Lett., 79 (1997), 893-896. |
[8] |
H. P. Fischer, P. Maass and W. Dieterich, Diverging time and length scales of spinodal decomposition modes in thin flows, Europhys. Lett., 42 (1998), 49-54.
doi: 10.2986/tren.001-0349. |
[9] |
H. P. Fischer, J. Reinhard, W. Dieterich, J.-F. Gouyet, P. Maass, A. Majhofer and D. Reinel, Time-dependent density functional theory and the kinetics of lattice gas systems in contact with a wall, J. Chem. Phys., 108 (1998), 3028-3037. |
[10] |
G. Gilardi, A. Miranville and G. Schimperna, On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions, Commun. Pure Appl. Anal., 8 (2009), 881-912. |
[11] |
G. Gilardi, A. Miranville and G. Schimperna, Long time behavior of the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions, Chinese Ann. Math., Ser. B, 31 (2010), 679-712. |
[12] |
M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192. |
[13] |
G. R. Goldstein, A. Miranville and G. Schimperna, A Cahn-Hilliard model in a domain with non-permeable walls, Physica D, 240 (2011), 754-766. |
[14] |
R. Kenzler, F. Eurich, P. Maass, B. Rinn, J. Schropp, E. Bohl and W. Dieterich, Phase separation in confined geometries: Solving the Cahn-Hilliard equation with generic boundary conditions, Comput. Phys. Commun., 133 (2001), 139-157. |
[15] |
A. Miranville, Some generalizations of the Cahn-Hilliard equation, Asymptotic Anal., 22 (2000), 235-259. |
[16] |
A. Miranville, Consistent models of Cahn-Hilliard-Gurtin equations with Neumann boundary conditions, Physica D, 158 (2001), 233-257. |
[17] |
A. Miranville, Generalized Cahn-Hilliard equations based on a microforce balance, J. Appl. Math., 2003 (2003), 165-185. |
[18] |
A. Miranville and S. Zelik, Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions, Math. Methods Appl. Sci., 28 (2005), 709-735. |
[19] |
A. Novick-Cohen, The Cahn-Hilliard equation: Mathematical and modeling perspectives, Adv. Math. Sci. Appl, 8 (1998), 965-985. |
[20] |
A. Novick-Cohen, The Cahn-Hilliard equation, in "Handbook of Differential Equations, Evolutionary Partial Differential Equations" (eds. C. M. Dafermos and M. Pokorny), 4, Elsevier, Amsterdam, (2008), 201-228. |
[21] |
J. Prüss, R. Racke and S. Zheng, Maximal regularity and asymptotic behavior of solutions for the Cahn-Hilliard equation with dynamic boundary conditions, Ann. Mat. Pura Appl. (4), 185 (2006), 627-648. |
[22] |
R. Racke and S. Zheng, The Cahn-Hilliard equation with dynamic boundary conditions, Adv. Diff. Eqns., 8 (2003), 83-110. |
[23] |
H. Wu and S. Zheng, Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions, J. Diff. Eqns., 204 (2004), 511-531. |
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