A Cahn-Hilliard-Gurtin model with dynamic boundary conditions

Gisèle Ruiz Goldstein; Alain Miranville

doi:10.3934/dcdss.2013.6.387

Article Contents

2013, Volume 6, Issue 2: 387-400. Doi: 10.3934/dcdss.2013.6.387

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A Cahn-Hilliard-Gurtin model with dynamic boundary conditions

Gisèle Ruiz Goldstein^1, and
Alain Miranville^2,

1.
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152
2.
Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, 86962 Chasseneuil Futuroscope Cedex

Received: August 31, 2011

Revised: September 30, 2011

Published: March 2013

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Abstract

Our aim in this paper is to define proper dynamic boundary conditions for a generalization of the Cahn-Hilliard system proposed by M. Gurtin. Such boundary conditions take into account the interactions with the walls in confined systems. We then study the existence and uniqueness of weak solutions.

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Mathematics Subject Classification: 35K55.

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References

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