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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

Ciprian G. Gal 1,

1. 

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

Received  March 2007 Revised  January 2008 Published  April 2008

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