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The polarization in a ferroelectric thin film: local and nonlocal limit problems

Published online by Cambridge University Press:  28 March 2013

Antonio Gaudiello  and
Kamel Hamdache
Antonio Gaudiello
Affiliation:
DIEI, Università degli Studi di Cassino e del Lazio meridionale, via G. Di Biasio 43, 03043 Cassino (FR), Italia. gaudiell@unina.it
Kamel Hamdache
Affiliation:
Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France; kamel.hamdache@polytechnique.edu
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Abstract

In this paper, starting from classical non-convex and nonlocal 3D-variational model of the electric polarization in a ferroelectric material, via an asymptotic process we obtain a rigorous 2D-variational model for a thin film. Depending on the initial boundary conditions, the limit problem can be either nonlocal or local.

Keywords

Electric polarizationthin filmnonlocal problems
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 3 , July 2013 , pp. 657 - 667
Copyright
© EDP Sciences, SMAI, 2013

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