Details
| Original language | English |
|---|---|
| Pages (from-to) | 389-417 |
| Number of pages | 29 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 211 |
| Issue number | 2 |
| Publication status | Published - 6 Jul 2013 |
Abstract
The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right-hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time, while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Mathematics (miscellaneous)
- Engineering(all)
- Mechanical Engineering
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In: Archive for Rational Mechanics and Analysis, Vol. 211, No. 2, 06.07.2013, p. 389-417.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Parabolic Free Boundary Problem Modeling Electrostatic MEMS
AU - Escher, Joachim
AU - Laurençot, Philippe
AU - Walker, Christoph
PY - 2013/7/6
Y1 - 2013/7/6
N2 - The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right-hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time, while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.
AB - The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right-hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time, while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.
UR - http://www.scopus.com/inward/record.url?scp=84892440800&partnerID=8YFLogxK
U2 - 10.1007/s00205-013-0656-2
DO - 10.1007/s00205-013-0656-2
M3 - Article
AN - SCOPUS:84892440800
VL - 211
SP - 389
EP - 417
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 2
ER -