Electron. J. Diff. Eqns., Vol. 2006(2006), No. 143, pp. 1-23.

Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls

Ciprian G. Gal

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.

Submitted August 30, 2006. Published November 16, 2006.
Math Subject Classifications: 35K55, 74N20, 35B40, 35B45, 37L30.
Key Words: Phase separation; Cahn-Hilliard equations; dynamic boundary conditions; exponential attractors; global attractors; Laplace-Beltrami differential operators.

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Ciprian G. Gal
Department of Mathematical Sciences
Uinversity of Memphis
Memphis, TN 38152, USA
email: cgal@memphis.edu

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