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 λ. It is shown that there is a threshold value λ*>0 of the voltage parameter such that no radially symmetric stationary solution exists for λ>λ*, while at least two such solutions exist for λ∈(0,λ*). 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 λ>λ*.