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

Antonio Gaudiello; Kamel Hamdache

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 3, page 657-667
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Gaudiello, Antonio, and Hamdache, Kamel. "The polarization in a ferroelectric thin film: local and nonlocal limit problems." ESAIM: Control, Optimisation and Calculus of Variations 19.3 (2013): 657-667. <http://eudml.org/doc/272781>.

@article{Gaudiello2013,
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.},
author = {Gaudiello, Antonio, Hamdache, Kamel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {electric polarization; thin film; nonlocal problems},
language = {eng},
number = {3},
pages = {657-667},
publisher = {EDP-Sciences},
title = {The polarization in a ferroelectric thin film: local and nonlocal limit problems},
url = {http://eudml.org/doc/272781},
volume = {19},
year = {2013},
}

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
PB - EDP-Sciences
VL - 19
IS - 3
SP - 657
EP - 667
AB - 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.
LA - eng
KW - electric polarization; thin film; nonlocal problems
UR - http://eudml.org/doc/272781
ER -

References

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  10. [10] G. Gioia and R.D. James, Micromagnetism of very thin films. Proc. of R. London A453 (1997) 213–223. 
  11. [11] R.V. Kohn and V.V. Slastikov, Another thin-film limit of micromagnetics. Arch. Ration. Mech. Anal.178 (2005) 227–245. Zbl1074.78012MR2186425
  12. [12] R.C. Smith, Smart material systems. model development, in Front. Appl. Math. Vol. 32. SIAM (2005). Zbl1086.74002MR2132740
  13. [13] Y. Su and C.M. Landis, Continuum thermodynamics of ferroelectric domain evolution: theory, finite element implementation, and application to domain wall pinning. J. Mech. Phys. Solids55 (2007) 280–305. Zbl05560696MR2287644
  14. [14] W. Zhang and K. Bhattacharya, A computational model of ferroelectric domains. Part I. Model formulation and domain switching. Acta Mater. 53 (2005) 185–198. 

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