A fourth‐order model for MEMS with clamped boundary conditions. Issue 6 (22nd July 2014)

• Record Type: Journal Article
• Authors: Laurençot, Philippe; Walker, Christoph
• Is Part Of: Proceedings of the London Mathematical Society. Volume 109:Issue 6(2014:Dec.)
• Page Start: 1435
• Page End: 1464
• Publication Date: 2014-07-22
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms/pdu037
• Languages: English
• ISSNs: 0024-6115

Abstract

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 * .