  The evolution problem for a membrane based model of an electrostatically
actuated microelectromechanical system (MEMS) is studied. The model describes
the dynamics of the membrane displacement and the electric potential. The
latter is a harmonic function in an angular domain, the deformable membrane
being a part of the boundary. The former solves a heat equation with a right
hand side that depends on the square of the trace of the gradient of the
electric potential on the membrane. The resulting free boundary problem is
shown to be well-posed locally in time. Furthermore, solutions corresponding to
small voltage values exist globally in time while global existence is shown not
to hold for high voltage values. It is also proven that, for small voltage
values, there is an asymptotically stable steady-state solution. Finally, the
small aspect ratio limit is rigorously justified.
