A fourth-order model for MEMS with clamped boundary conditions

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 (MEMS) and includes a positive voltage parameter $\lambda$. It is shown that there is a threshold value ${\lambda }_{\ast }>0$ of the voltage parameter such that no radially symmetric stationary solution exists for $\lambda >{\lambda }_{\ast }$, while at least two such solutions exist for $\lambda \in (0,{\lambda }_{\ast })$. 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 $\lambda >{\lambda }_{\ast }$.

References in corpus (4)

• The critical dimension for a 4th order problem with singular nonlinearity
• Multiple Quenching Solutions of a Fourth Order Parabolic PDE with a singular nonlinearity modelling a MEMS Capacitor
• A stationary free boundary problem modeling electrostatic MEMS
• Sign-Preserving Property for Some Fourth-Order Elliptic Operators in One Dimension and Radial Symmetry