JournalsifbVol. 18, No. 3pp. 393–411

On a three-dimensional free boundary problem modeling electrostatic MEMS

  • Philippe Laurençot

    Université de Toulouse, Toulouse, France
  • Christoph Walker

    Leibniz-Universität Hannover, Germany
On a three-dimensional free boundary problem modeling electrostatic MEMS cover
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Abstract

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 the electrostatic potential on this plate. The strength of the coupling is tuned by a parameter  proportional to the square of the applied voltage. We prove that this free boundary problem is locally well-posed in time and that for small values of  solutions exist globally in time. We also derive the existence of a branch of asymptotically stable stationary solutions for small values of  and non-existence of stationary solutions for large values thereof, the latter being restricted to a disc-shaped plate.

Cite this article

Philippe Laurençot, Christoph Walker, On a three-dimensional free boundary problem modeling electrostatic MEMS. Interfaces Free Bound. 18 (2016), no. 3, pp. 393–411

DOI 10.4171/IFB/368