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arXiv · 1304.2296

A fourth-order model for MEMS with clamped boundary conditions

Philippe Laurencot·Christoph Walker
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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 $λ$. It is shown that there is a threshold value $λ_*>0$ of the voltage parameter such that no radially symmetric stationary solution exists for $λ>λ_*$, while at least two such solutions exist for $λ\in (0,λ_*)$. 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 when $λ>λ_*$.

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Philippe Laurencot, Christoph Walker. 2013-04-08. A fourth-order model for MEMS with clamped boundary conditions. https://doi.org/10.1112/plms%2Fpdu037

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