A free boundary value problem modelling microelectromechanical systems with general permittivity. (October 2015)

• Record Type: Journal Article
• Authors: Lienstromberg, Christina
• Is Part Of: Nonlinear analysis. Volume 25(2015)
• Page Start: 190
• Page End: 218
• Publication Date: 2015-10
• Subjects: MEMS -- General permittivity profile -- Well-posedness -- Small-aspect ratio limit; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.03.008
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: An investigation of the free boundary value problem arising from the modelling of electrostatically actuated microelectromechanical systems with general permittivity is presented. Consisting of a parabolic evolution problem for the displacement of a membrane as well as of an elliptic moving boundary problem for the electric potential between the membrane and a rigid ground plate, the system is shown to be well-posed locally in time for all values λ of the applied voltage. It is in addition verified that the solution exists even globally in time, provided that the applied voltage does not exceed a certain critical value λ ∗ . Furthermore, we establish the convergence of the solution of the free boundary problem towards the solution of the small-aspect ratio model, as the aspect ratio tends to zero.