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

Abstract

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.

Keywords

• Phase separation
• Cahn-Hilliard equations
• dynamic boundary conditions
• exponential attractors
• global attractors
• Laplace-Beltrami differential operators.