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Global existence via a multivalued operator for an Allen-Cahn-Gurtin equation
1. | ENS Cachan Bretagne, IRMAR, EUB, Campus de Ker Lann, 35170 Bruz |
2. | Université de Poitiers, Laboratoire de Mathématiques, et Applications UMR CNRS 7348, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France |
References:
[1] |
H. Abels and M. Wilke, Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy, Nonlinear Anal., 67 (2007), 3176-3193.
doi: 10.1016/j.na.2006.10.002. |
[2] |
H. Brezis, "Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert," North-Holland Publishing Co., Amsterdam, 1973. |
[3] |
H. Brezis and F. Browder, Sur une propriété des espaces de Sobolev, C. R. Acad. Sci. Paris, 287 (1978), 113-115. |
[4] |
T. Cazenave and A. Haraux, "Introduction aux Problèmes D'évolution Semi-Linéaires," Mathématiques & Applications (Paris), 1, Ellipses, Paris, 1990. |
[5] |
L. Cherfils and A. Miranville, Finite dimensional attractors for a model of Allen-Cahn equation based on a microforce balance, C. R. Acad. Sci. Paris, Sér. I, Math., 329 (1999), 1109-1114.
doi: 10.1016/S0764-4442(00)88483-9. |
[6] |
L. Cherfils and Mo. Pierre, Non-global existence for an Allen-Cahn-Gurtin equation with logarithmic free energy, J. Evol. Equ., 8 (2008), 727-748.
doi: 10.1007/s00028-008-0412-5. |
[7] |
E. DiBenedetto and Mi. Pierre, On the maximum principle for pseudoparabolic equations, Indiana Univ. Math. J., 30 (1981), 821-854.
doi: 10.1512/iumj.1981.30.30062. |
[8] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin, 2001. |
[9] |
M. Grun-Rehomme, Caractérisation du sous-différentiel d'intégrandes convexes dans les espaces de Sobolev, J. Math. Pures et Appl., 56 (1977), 149-156. |
[10] |
M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Phys. D, 92 (1996), 178-192.
doi: 10.1016/0167-2789(95)00173-5. |
[11] |
A. Henrot et Mi. Pierre, "Variation et Optimisation de Formes: Une Analyse Géométrique," Mathématiques & Applications 48, Springer, 2005. |
[12] |
J.-L. Lions, "Quelques Méthodes de Résolution de Problèmes aux Limites non Linéaires," Dunod., 1969. |
[13] |
A. Miranville, A model of Cahn-Hilliard equation based on a microforce balance, C. R. Acad. Sci. Paris Sér. I Math., 328 (1999), 1247-1252.
doi: 10.1016/S0764-4442(99)80448-0. |
[14] |
V. Thomée, "Galerkin Finite Element Methods for Parabolic Problems," Springer Series in Computational Mathematics, 25, Springer-Verlag, Berlin, 2006. |
show all references
References:
[1] |
H. Abels and M. Wilke, Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy, Nonlinear Anal., 67 (2007), 3176-3193.
doi: 10.1016/j.na.2006.10.002. |
[2] |
H. Brezis, "Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert," North-Holland Publishing Co., Amsterdam, 1973. |
[3] |
H. Brezis and F. Browder, Sur une propriété des espaces de Sobolev, C. R. Acad. Sci. Paris, 287 (1978), 113-115. |
[4] |
T. Cazenave and A. Haraux, "Introduction aux Problèmes D'évolution Semi-Linéaires," Mathématiques & Applications (Paris), 1, Ellipses, Paris, 1990. |
[5] |
L. Cherfils and A. Miranville, Finite dimensional attractors for a model of Allen-Cahn equation based on a microforce balance, C. R. Acad. Sci. Paris, Sér. I, Math., 329 (1999), 1109-1114.
doi: 10.1016/S0764-4442(00)88483-9. |
[6] |
L. Cherfils and Mo. Pierre, Non-global existence for an Allen-Cahn-Gurtin equation with logarithmic free energy, J. Evol. Equ., 8 (2008), 727-748.
doi: 10.1007/s00028-008-0412-5. |
[7] |
E. DiBenedetto and Mi. Pierre, On the maximum principle for pseudoparabolic equations, Indiana Univ. Math. J., 30 (1981), 821-854.
doi: 10.1512/iumj.1981.30.30062. |
[8] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin, 2001. |
[9] |
M. Grun-Rehomme, Caractérisation du sous-différentiel d'intégrandes convexes dans les espaces de Sobolev, J. Math. Pures et Appl., 56 (1977), 149-156. |
[10] |
M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Phys. D, 92 (1996), 178-192.
doi: 10.1016/0167-2789(95)00173-5. |
[11] |
A. Henrot et Mi. Pierre, "Variation et Optimisation de Formes: Une Analyse Géométrique," Mathématiques & Applications 48, Springer, 2005. |
[12] |
J.-L. Lions, "Quelques Méthodes de Résolution de Problèmes aux Limites non Linéaires," Dunod., 1969. |
[13] |
A. Miranville, A model of Cahn-Hilliard equation based on a microforce balance, C. R. Acad. Sci. Paris Sér. I Math., 328 (1999), 1247-1252.
doi: 10.1016/S0764-4442(99)80448-0. |
[14] |
V. Thomée, "Galerkin Finite Element Methods for Parabolic Problems," Springer Series in Computational Mathematics, 25, Springer-Verlag, Berlin, 2006. |
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