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A fourth-order model for MEMS with clamped boundary conditions (2014)

Laurencot, P., Walker, C.

Oxford University Press

In: Proceedings of the London Mathematical Society

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Publication Date: 2014-12-17

Description: 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 $\lambda$ . It is shown that there is a threshold value $\lambda _* 〉 0$ of the voltage parameter such that no radially symmetric stationary solution exists for $\lambda 〉 \lambda _* $ , while at least two such solutions exist for $\lambda \in (0,\lambda _* )$ . 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 _* $ .

Print ISSN: 0024-6115

Electronic ISSN: 1460-244X

Topics: Mathematics

Published by Oxford University Press

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