  The dynamics of a free boundary problem for electrostatically actuated
microelectromechanical systems (MEMS) is investigated. The model couples the
electric potential to the deformation of the membrane, the deflection of the
membrane being caused by application of a voltage difference across the device.
More precisely, the electrostatic potential is a harmonic function in the
angular domain that is partly bounded by the deformable membrane. The gradient
trace of the electric potential on this free boundary part acts as a source
term in the governing equation for the membrane deformation. The main feature
of the model considered herein is that, unlike most previous research, the
small deformation assumption is dropped, and curvature for the deformation of
the membrane is taken into account what leads to a quasilinear parabolic
equation. The free boundary problem is shown to be well-posed, locally in time
for arbitrary voltage values and globally in time for small voltages values.
Furthermore, existence of asymptotically stable steady-state configurations is
proved in case of small voltage values as well as non-existence of
steady-states if the applied voltage difference is large. Finally, convergence
of solutions of the free boundary problem to the solutions of the
well-established small aspect ratio model is shown.
