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Well-posedness and long time behavior of an Allen-Cahn type equation
1. | UMR 6086 CNRS. Laboratoire de Mathématiques et Applications - Université de Poitiers, SP2MI - Boulevard Marie et Pierre Curie - Téléport 2, BP30179 - 86962 Futuroscope Chasseneuil Cedex, France |
References:
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A. Bonfoh and A. Miranville, On Cahn-Hilliard-Gurtin equations,, in, 47 (2001), 3455.
doi: 10.1016/S0362-546X(01)00463-1. |
[2] |
M. Carrive, A. Miranville, A. Piétrus and J. M. Rakotoson, Weakly coupled dynamical systems and applications,, Asymptotic Analysis, 30 (2002), 161.
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[3] |
A. Eden, C. Foias, B. Nicolaenko and R. and Temam, "Exponential Attractors for Dissipative Evolution Equations,", Masson, (1994).
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[4] |
M.Efendiev, A. Miranville and S. Zelik, Exponential attractors for a singularly perturbed Cahn-Hilliard system,, Math. Nachr., 272 (2004), 11.
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[5] |
G. Karali, and A. Katsoulakis, The role of multiple microscopic mechanisms in cluster interface evolution,, J. Differential Equations, 235 (2007), 418.
doi: 10.1016/j.jde.2006.12.021. |
[6] |
G. Karali and T. Ricciardi, On the convergence of a fourth order evolution equation to the Allen-Cahn equation,, Nonlinear Anal., 72 (2010), 4271.
doi: 10.1016/j.na.2010.02.003. |
[7] |
A. Katsoulakis and G. Vlachos, From microscopic interactions to macroscopic laws of cluster evolution,, Phys. Rev. Lett., 84 (2000), 1511.
doi: 10.1103/PhysRevLett.84.1511. |
[8] |
S. Mikhailov, M. Hildebrand and G. Ertl, Nonequilibrium nanostructures in condensed reactive systems,, in, 567 (2001), 252.
doi: 10.1007/3-540-44698-2_16. |
[9] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains,, in, (2008), 103.
doi: 10.1016/S1874-5717(08)00003-0. |
[10] |
A. Miranville, Some generalizations of the Cahn-Hilliard equation,, Asymptot. Anal., 22 (2000), 235.
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[11] |
A. Miranville, Long-time behavior of some models of Cahn-Hilliard equations in deformable continua,, Nonlinear Anal. Real World Appl., 2 (2001), 273.
doi: 10.1016/S0362-546X(00)00104-8. |
[12] |
C. Robinson, "Infinite-dimensional Dynamical Systems,'', Cambridge Universtity Press, (2001).
|
[13] |
R. Temam, "Infinite-dimensional Dynamical Systems in Mechanics and Physics,'', Springer-Verlag, (1988).
doi: 10.1007/978-1-4684-0313-8. |
show all references
References:
[1] |
A. Bonfoh and A. Miranville, On Cahn-Hilliard-Gurtin equations,, in, 47 (2001), 3455.
doi: 10.1016/S0362-546X(01)00463-1. |
[2] |
M. Carrive, A. Miranville, A. Piétrus and J. M. Rakotoson, Weakly coupled dynamical systems and applications,, Asymptotic Analysis, 30 (2002), 161.
|
[3] |
A. Eden, C. Foias, B. Nicolaenko and R. and Temam, "Exponential Attractors for Dissipative Evolution Equations,", Masson, (1994).
|
[4] |
M.Efendiev, A. Miranville and S. Zelik, Exponential attractors for a singularly perturbed Cahn-Hilliard system,, Math. Nachr., 272 (2004), 11.
|
[5] |
G. Karali, and A. Katsoulakis, The role of multiple microscopic mechanisms in cluster interface evolution,, J. Differential Equations, 235 (2007), 418.
doi: 10.1016/j.jde.2006.12.021. |
[6] |
G. Karali and T. Ricciardi, On the convergence of a fourth order evolution equation to the Allen-Cahn equation,, Nonlinear Anal., 72 (2010), 4271.
doi: 10.1016/j.na.2010.02.003. |
[7] |
A. Katsoulakis and G. Vlachos, From microscopic interactions to macroscopic laws of cluster evolution,, Phys. Rev. Lett., 84 (2000), 1511.
doi: 10.1103/PhysRevLett.84.1511. |
[8] |
S. Mikhailov, M. Hildebrand and G. Ertl, Nonequilibrium nanostructures in condensed reactive systems,, in, 567 (2001), 252.
doi: 10.1007/3-540-44698-2_16. |
[9] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains,, in, (2008), 103.
doi: 10.1016/S1874-5717(08)00003-0. |
[10] |
A. Miranville, Some generalizations of the Cahn-Hilliard equation,, Asymptot. Anal., 22 (2000), 235.
|
[11] |
A. Miranville, Long-time behavior of some models of Cahn-Hilliard equations in deformable continua,, Nonlinear Anal. Real World Appl., 2 (2001), 273.
doi: 10.1016/S0362-546X(00)00104-8. |
[12] |
C. Robinson, "Infinite-dimensional Dynamical Systems,'', Cambridge Universtity Press, (2001).
|
[13] |
R. Temam, "Infinite-dimensional Dynamical Systems in Mechanics and Physics,'', Springer-Verlag, (1988).
doi: 10.1007/978-1-4684-0313-8. |
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