The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions

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March 2010, 28(1): 275-310. doi: 10.3934/dcds.2010.28.275

The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions

Alain Miranville ^1, and Sergey Zelik ^2,

1.	Université de Poitiers, Laboratoire de Mathématiques et Applications, SP2MI, 86962 Chasseneuil Futuroscope Cedex, France
2.	Department of Mathematics, University of Surrey, Guildford, GU2 7XH

Received April 2009 Revised August 2009 Published April 2010

Abstract
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Our aim in this paper is to study the Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. In particular, we prove, owing to proper approximations of the singular potential and a suitable notion of variational solutions, the existence and uniqueness of solutions. We also discuss the separation of the solutions from the singularities of the potential. Finally, we prove the existence of global and exponential attractors.

Keywords: singular potentials, global attractor, variational solutions, dynamic boundary conditions, Cahn-Hilliard equation, exponential attractors., separation from the singularities.

Mathematics Subject Classification: 35B40, 35B41, 35K55, 35J60, 80A2.

Citation: Alain Miranville, Sergey Zelik. The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 275-310. doi: 10.3934/dcds.2010.28.275

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