# A fourth-order model for MEMS with clamped boundary conditions

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1 IMT - Institut de Mathématiques de Toulouse UMR5219 2 IFAM - Institut für Angewandte Mathematik

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 $\lambda *>0$ 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 $\lambda>\lambda *$.

Keywords : touchdown positivity quenching MEMS fourth-order diffusion beam equation

Autor: Philippe Laurencot - Christoph Walker -

Fuente: https://hal.archives-ouvertes.fr/

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