Geodesic
Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls
Electronic journal of differential equations, Tome 2006 (2006)
In a previous article [7], we proposed a model of phase separation in a binary mixture confined to a bounded region which may be contained within porous walls. The boundary conditions were derived from a mass conservation law and variational methods. In the present paper, we study the problem further. Using a Faedo-Galerkin method, we obtain the existence and uniqueness of a global solution to our problem, under more general assumptions than those in [7]. We then study its asymptotic behavior and prove the existence of an exponential attractor (and thus of a global attractor) with finite dimension.
Classification : 35K55, 74N20, 35B40, 35B45, 37L30
Keywords: phase separation, Cahn-Hilliard equations, dynamic boundary conditions, exponential attractors, global attractors, Laplace-Beltrami differential operators 
@article{EJDE_2006__2006__a159,
     author = {Gal,  Ciprian G.},
     title = {Exponential attractors for a {Cahn-Hilliard} model in bounded domains with permeable walls},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1113.35031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a159/}
}
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Gal,  Ciprian G. Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a159/