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.


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


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