Finite-Time Singularities of Solutions to Microelectromechanical Systems with General Permittivity

Of concern is a study of qualitative properties of solutions to the evolution problem modelling microelectromechanical systems with general permittivity. The system couples a quasilinear parabolic evolution problem for a membrane's displacement with an elliptic free boundary value problem for the electrostatic potential in the region between the membrane and a rigid ground plate. It is shown that, under a structural condition on the permittivity profile, non-positive solutions develop a singularity in finite time, provided that the applied voltage is large enough and the aspect ratio of the system is small enough.