Vol. 63, No. 4, pp. 375-392 (2006)
Asymptotic behavior of thin ferroelectric materials
Naïma AïssaCentre de Mathématiques Appliquées,
CNRS UMR 7641, Ecole Polytechnique, 91128 Palaiseau Cedex -- FRANCE
Faculté des Mathématiques, U.S.T.H.B,
BP 32, El Alia 16111 Alger -- ALGÉRIE
Abstract: We are dealing with the model of ferroelectric materials that has been introduced by J.M. Greenberg and Al in Physica D 134, 362--383 (1999). We suppose that the ferroelectric material occupies a thin cylinder with regular cross section and small thickness $\nu>0$ and give the limit model as $\nu$ goes to $0$. Linear and nonlinear potentials are considered. In both cases, one notices that the limit problem is sensitive to the choice of the boundary conditions. We observe that Silver--Müller boundary conditions induce new terms in the limit problems.
Keywords: Maxwell equations; ferroelectric materials; thin cylinders.
Classification (MSC2000): 35L10, 35K05.
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Electronic version published on: 7 Mar 2008.