Abstract

AbstractWe consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential. We first review some recent results on existence and nonexistence of steady states as well as on local and global well-posedness of the dynamical problem, the main focus being on the possible touchdown behavior of the elastic plate. We then investigate the behavior of the solutions in the time singular limit, when the ratio between inertial and damping effects decays to zero.KeywordsMicroelectromechanical Systems (MEMS)Elastic PlatePlate DisplacementGlobal Well-posednessFree Boundary ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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