Volume 19, Number 3, July-September 2013
|Page(s)||657 - 667|
|Published online||28 March 2013|
The polarization in a ferroelectric thin film: local and nonlocal limit problems
DIEI, Università degli Studi di Cassino e del Lazio
meridionale, via G. Di Biasio
Cassino ( FR), Italia
2 Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France
Revised: 22 May 2012
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.
Mathematics Subject Classification: 35Q61 / 78A25
Key words: Electric polarization / thin film / nonlocal problems
© EDP Sciences, SMAI, 2013
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