The Cahn-Hilliard equation with singular potentials and dynamicboundary conditions

Alain Miranville; Sergey Zelik

doi:10.3934/dcds.2010.28.275

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2010, Volume 28, Issue 1: 275-310. Doi: 10.3934/dcds.2010.28.275

This issue Previous Article Models & measures of mixing & effective diffusion Next Article Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation

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
2.
Department of Mathematics, University of Surrey, Guildford, GU2 7XH

Received: March 31, 2009

Revised: July 31, 2009

Published: February 2010

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Abstract

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.

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Mathematics Subject Classification: 35B40, 35B41, 35K55, 35J60, 80A22.

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