Abstract and Applied Analysis
Volume 2007 (2007), Article ID 61629, 14 pages
Research Article

Asymptotics of Time Harmonic Solutions to a Thin Ferroelectric Model

Naïma Aïssa1,2 and Kamel Hamdache1

1Centre de Mathématiques Appliquées (CMAP), UMR 7641 CNRS, Ecole Polytechnique, Palaiseau Cedex 91128, France
2Faculté de Mathématiques, Université des Sciences et de la Technologie Houari Boumediene (USTHB), BP 32, Bab Ezzouar, Alger 16123, Algeria

Received 19 April 2005; Revised 31 January 2007; Accepted 1 February 2007

Academic Editor: Nicholas Dimitrios Alikakos

Copyright © 2007 Naïma Aïssa and Kamel Hamdache. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce new model equations to describe the dynamics of the electric polarization in a ferroelectric material. We consider a thin cylinder representing the material with thickness ɛ and discuss the asymptotic behavior of the time harmonic solutions to the model when ɛ tends to 0. We obtain a reduced model settled in the cross-section of the cylinder describing the dynamics of the plane components of the polarization and electric fields.