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.
1
Université de Toulouse, Toulouse, France
2
Leibniz-Universität Hannover, Germany
Philippe Laurençot; Christoph Walker. On a three-dimensional free boundary problem modeling electrostatic MEMS. Interfaces and free boundaries, Tome 18 (2016) no. 3, pp. 393-411. doi: 10.4171/ifb/368
@article{10_4171_ifb_368,
author = {Philippe Lauren\c{c}ot and Christoph Walker},
title = {On a three-dimensional free boundary problem modeling electrostatic {MEMS}},
journal = {Interfaces and free boundaries},
pages = {393--411},
year = {2016},
volume = {18},
number = {3},
doi = {10.4171/ifb/368},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/368/}
}
TY - JOUR
AU - Philippe Laurençot
AU - Christoph Walker
TI - On a three-dimensional free boundary problem modeling electrostatic MEMS
JO - Interfaces and free boundaries
PY - 2016
SP - 393
EP - 411
VL - 18
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/368/
DO - 10.4171/ifb/368
ID - 10_4171_ifb_368
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%J Interfaces and free boundaries
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%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/368/
%R 10.4171/ifb/368
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