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Asymptotics of time harmonic solutions to a thin ferroelectric model. (English) Zbl 1157.35485

Summary: We introduce new model equations to describe the dynamics of the electric polarization in a ferroelectric material. We consider a thin cylinder representing the material with thickness \(\varepsilon \) and discuss the asymptotic behavior of the time harmonic solutions to the model when \(\varepsilon \) tends to 0. We obtain a reduced model settled in the cross-section of the cylinder describing the dynamics of the plane components of the polarization and electric fields.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
35B40 Asymptotic behavior of solutions to PDEs
82D45 Statistical mechanics of ferroelectrics
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