- journal article metadata
European Mathematical Society Publishing House
2016-10-17 23:45:01
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
18
2016
3
On a three-dimensional free boundary problem modeling electrostatic MEMS
Philippe
Laurençot
Université de Toulouse, TOULOUSE CEDEX 9, FRANCE
Christoph
Walker
Leibniz-Universität Hannover, HANNOVER, GERMANY
MEMS, free boundary problem, stationary solutions
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.
Partial differential equations
393
411
10.4171/IFB/368
http://www.ems-ph.org/doi/10.4171/IFB/368