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

Date

2006-11-16

Authors

Gal, Ciprian G.

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Publisher

Texas State University-San Marcos, Department of Mathematics

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.

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Keywords

Phase separation, Cahn-Hilliard equations, Dynamic boundary conditions, Exponential attractors, Global attractors, Laplace-Beltrami differential operators

Citation

Gal, C. G. (2006). Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls. <i>Electronic Journal of Differential Equations, 2006</i>(143), pp. 1-23.

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Attribution 4.0 International

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