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Zeitschrift für Analysis und ihre Anwendungen


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Volume 37, Issue 2, 2018, pp. 209–219
DOI: 10.4171/ZAA/1610

Published online: 2018-03-29

Finite Time Singularity in a MEMS Model Revisited

Philippe Laurençot[1] and Christoph Walker[2]

(1) Université de Toulouse, France
(2) Leibniz Universität Hannover, Germany

A free boundary problem modeling a microelectromechanical system consisting of a fixed ground plate and a deformable top plate is considered, the plates being held at di fferent electrostatic potentials. It couples a second order semilinear parabolic equation for the deformation of the top plate to a Laplace equation for the electrostatic potential in the device. The validity of the model is expected to break down in finite time when the applied voltage exceeds a certain value, a finite time singularity occurring then. This result, already known for non-positive initial con figurations of the top plate, is here proved for arbitrary ones and thus now includes, in particular, snap-through instabilities.

Keywords: MEMS, free boundary problem, finite time singularity

Laurençot Philippe, Walker Christoph: Finite Time Singularity in a MEMS Model Revisited. Z. Anal. Anwend. 37 (2018), 209-219. doi: 10.4171/ZAA/1610