| Issue |
ESAIM: COCV
Volume 19, Number 3, July-September 2013
|
|
|---|---|---|
| Page(s) | 657 - 667 | |
| DOI | https://doi.org/10.1051/cocv/2012026 | |
| Published online | 28 March 2013 | |
The polarization in a ferroelectric thin film: local and nonlocal limit problems
1
DIEI, Università degli Studi di Cassino e del Lazio
meridionale, via G. Di Biasio
43, 03043
Cassino ( FR), Italia
gaudiell@unina.it
2
Centre de Mathématiques Appliquées, École
Polytechnique, 91128
Palaiseau,
France
kamel.hamdache@polytechnique.edu
Received:
17
January
2012
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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