Abstract
We consider a mathematical model describing polarization dynamics in ferroelectric material. The model consists of a Maxwell system for electromagnetic field coupled with a second-order time-dependent equation for the evolution of polarization. We study the long-time behaviour of weak solutions and prove that all points of the ω-limit set of any trajectories are solutions of the stationary model.
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Acknowledgements
This work was supported by the PHC Volubilis programme MA/14/301 “Elaboration et analyse de modèles asymptotiques en micro-magnétisme, magnéto-élasticité et électro-élasticité” with joint financial support from the French Ministry of Foreign Affairs and the Moroccan Ministry of Higher Education and Scientific Research.
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Aouragh, M.D., Hadda, M., Tilioua, M. (2016). On Polarization Dynamics in Ferroelectric Materials. In: Pinelas, S., Došlá, Z., Došlý, O., Kloeden, P. (eds) Differential and Difference Equations with Applications. ICDDEA 2015. Springer Proceedings in Mathematics & Statistics, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-319-32857-7_25
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DOI: https://doi.org/10.1007/978-3-319-32857-7_25
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