Asymptotic behavior of thin ferroelectric models
Year: 2025
Type: article
Abstract: It was pointed out in Shaw et al. (2000) that the boundary conditions satisfied by the polarization play an important role in the description of the thin-limit of ferroelectric materials . In this work we confirm the importance of this choice. In the present work, we consider the limiting process as the thickness h of a thin cylinder of R 3 goes to 0, and when the polarization satisfies two different boundary conditions. The first type of boundary conditions leads to an in-plane model or 2 d − 2 d configuration while the second one leads to an (in-plane)-(out-of-plane) model for the displacement and the polarization namely a 2 d − 3 d configuration. Moreover, the thin-limit process in both cases induces a change of the Lamé coefficients in the displacement equation, the coupling coefficient between the displacement and polarization equations, the double wells potential of the polarization together to a new contribution in the equation of the out-of-plane component of the polarization for the 2 d − 3 d model. The techniques used rely on a rescaling method that penalizes the out-of-plane variable. Uniform bounds with respect to h are established, compactness techniques are employed, and the limits of the penalized terms are identified.
Authors: Kamel Hamdache, Djamila Hamroun
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,780
OpenAlex ID: W4409106537