The time singular limit for a fourth-order damped wave equation for MEMS

Philippe Laurencot (1) , Christoph Walker (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IFAM - Institut für Angewandte Mathematik

We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential. We first review some recent results on existence and non-existence of steady-states as well as on local and global well-posedness of the dynamical problem, the main focus being on the possible touchdown behavior of the elastic plate. We then investigate the behavior of the solutions in the time singular limit when the ratio between inertial and damping effects tends to zero.

Mots clés: MEMS; beam equation; singular limit

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurencot, Christoph Walker. The time singular limit for a fourth-order damped wave equation for MEMS. J. Escher, E. Schrohe, J. Seiler, Ch. Walker. Elliptic and Parabolic Equations. Hannover September 2013, 119, Springer, pp.233--246, 2015, Springer Proceedings in Mathematics and Statistics. ⟨hal-00983240⟩