  A parabolic free boundary problem modeling a three-dimensional electrostatic
MEMS device is investigated. The device is made of a rigid ground plate and an
elastic top plate which is hinged at its boundary, the plates being held at
different voltages. The model couples a fourth-order semilinear parabolic
equation for the deformation of the top plate to a Laplace equation for the
electrostatic potential in the device. The strength of the coupling is tuned by
a parameter $\lambda$ which is proportional to the square of the applied
voltage difference. It is proven that the model is locally well-posed in time
and that, for $\lambda$ sufficiently small, solutions exist globally in time.
In addition, touchdown of the top plate on the ground plate is shown to be the
only possible finite time singularity.
