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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.
@article{COCV_2013__19_3_657_0,
author = {Gaudiello, Antonio and Hamdache, Kamel},
title = {The polarization in a ferroelectric thin film: local and nonlocal limit problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {657--667},
publisher = {EDP-Sciences},
volume = {19},
number = {3},
year = {2013},
doi = {10.1051/cocv/2012026},
mrnumber = {3092355},
zbl = {1291.35384},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012026/}
}
TY - JOUR AU - Gaudiello, Antonio AU - Hamdache, Kamel TI - The polarization in a ferroelectric thin film: local and nonlocal limit problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 657 EP - 667 VL - 19 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012026/ DO - 10.1051/cocv/2012026 LA - en ID - COCV_2013__19_3_657_0 ER -
%0 Journal Article %A Gaudiello, Antonio %A Hamdache, Kamel %T The polarization in a ferroelectric thin film: local and nonlocal limit problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 657-667 %V 19 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012026/ %R 10.1051/cocv/2012026 %G en %F COCV_2013__19_3_657_0
Gaudiello, Antonio; Hamdache, Kamel. The polarization in a ferroelectric thin film: local and nonlocal limit problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 657-667. doi: 10.1051/cocv/2012026
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