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

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

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

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