Abstract
Qualitative properties of solutions to the evolution problem modelling microelectromechanical systems with general permittivity profile are investigated. The system couples a parabolic evolution problem for the displacement of a membrane with an elliptic free boundary value problem for the electric potential in the region between the membrane and a rigid ground plate. We briefly allude to results concerning local and global well-posedness and the small-apect ratio limit. However, the focus is here on proving non-positivity of the membrane displacement for the full moving boundary problem under certain boundary conditions on the potential, as well as the existence of finite-time singularities assuming to have a non-positive solution.
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