Touchdown is the Only Finite Time Singularity in a Three-Dimensional MEMS Model

摘要

Touchdown is shown to be the only possible finite time singularity that may take place in a free boundary problem modeling a three-dimensional microelectromechanical system. The proof relies on the energy structure of the problem and uses smoothing effects of the semigroup generated in L1 by the bi-Laplacian with clamped boundary conditions.