A fourth‐order model for MEMS with clamped boundary conditions. Issue 6 (22nd July 2014) - Laurençot, Philippe; Walker, Christoph
Abstract : 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 parameterλ . It is shown that there is a threshold valueλ * > 0 of the voltage parameter such that no radially symmetric stationary solution exists forλ > λ *, while at least two such solutions exist forλ ∈ ( 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 whenλ > λ * .