A fourth-order model for MEMS with clamped boundary conditions

The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems and includes a positive voltage parameter lambda. It is shown that there is a threshold value lambda(*) > 0 of the voltage parameter such that no radially symmetric stationary solution exists for lambda > lambda(*), while at least two such solutions exist for. lambda is an element of (0, lambda(*)). Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as the occurrence of finite time singularities when lambda > lambda(*).