On a three-dimensional free boundary problem modeling electrostatic MEMS

P. Laurençot & C. Walker
We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. While the existing literature focuses so far on a two-dimensional geometry, the present model considers a three-dimensional device where the harmonic electrostatic potential varies in the three-dimensional time-dependent region between the plates. The elastic plate deflection evolves according to a fourth-order semilinear parabolic equation which is coupled to the square of the gradient trace of...
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