Robust exponential attractors for a conserved Cahn-Hilliard model with singularly perturbed boundary conditions

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July 2008, 7(4): 819-836. doi: 10.3934/cpaa.2008.7.819

Robust exponential attractors for a conserved Cahn-Hilliard model with singularly perturbed boundary conditions

1.	Department of Mathematics, University of Missouri, Columbia, MO, 65211, United States

Received March 2007 Revised January 2008 Published April 2008

Abstract
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In this article, we construct a robust (that is, lower and upper semi-continuous) family of exponential attractors for a conserved Cahn-Hilliard model with the perturbation parameter in the boundary conditions. We note that the existence of a global attractor with finite dimension follows. Moreover, we prove the upper semi-continuity of the limiting attractor with respect to the family of perturbed global attractors.

Keywords: Cahn-Hilliard equations, singular perturbations., dynamic boundary conditions, exponential attractors, global attractors.

Mathematics Subject Classification: Primary: 35K55, 74N20, 35B40, 35B45, 37L3.

Citation: Ciprian G. Gal. Robust exponential attractors for a conserved Cahn-Hilliard model with singularly perturbed boundary conditions. Communications on Pure & Applied Analysis, 2008, 7 (4) : 819-836. doi: 10.3934/cpaa.2008.7.819

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