Asymptotics of Time Harmonic Solutions to a Thin Ferroelectric Model

Abstract

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.