Asymptotic behavior of thin ferroelectric materials

Naïma Aïssa

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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