Special Session 15: 

On Positivity of Solutions to Microelectromechanical Systems with General Permittivity Profile

Christina Lienstromberg
Leibniz University Hannover
Germany
Co-Author(s):    Joachim Escher, Pierre Gosselet
Abstract:
Qualitative properties of solutions to the evolution problem modelling microelectromechanical systems (MEMS) with general permittivity profile are investigated. The system couples a parabolic evolution problem for the displacement of a membrane with an elliptic moving boundary problem for the electric potential in the region between the membrane and a rigid ground plate. Conditions are specified which ensure non-positivity of the membrane`s displacement. Moreover, numerical evidence is provided for the existence of non-constant permittivity profiles that induce positive membrane displacements while the corresponding small-aspect ratio model possesses only non-positive displacements.