Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 209-219 |
Seitenumfang | 11 |
Fachzeitschrift | Zeitschrift fur Analysis und ihre Anwendung |
Jahrgang | 37 |
Ausgabenummer | 2 |
Publikationsstatus | Veröffentlicht - 30 März 2018 |
Abstract
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 different 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 nite time singularity occurring then. This result, already known for non-positive initial configurations of the top plate, is here proved for arbitrary ones and thus now includes, in particular, snap-through instabilities.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Ingenieurwesen (insg.)
- Allgemeiner Maschinenbau
- Volkswirtschaftslehre, Ökonometrie und Finanzen (insg.)
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: Zeitschrift fur Analysis und ihre Anwendung, Jahrgang 37, Nr. 2, 30.03.2018, S. 209-219.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Finite time singularity in a MEMS model revisited
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Funding Information: Acknowledgment. This work is partially supported by the French-German PROCOPE project 30718Z. Part of this work was done while PhL enjoyed the hospitality of the Institut für Angewandte Mathematik, Leibniz Universität Hannover.
PY - 2018/3/30
Y1 - 2018/3/30
N2 - 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 different 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 nite time singularity occurring then. This result, already known for non-positive initial configurations of the top plate, is here proved for arbitrary ones and thus now includes, in particular, snap-through instabilities.
AB - 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 different 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 nite time singularity occurring then. This result, already known for non-positive initial configurations of the top plate, is here proved for arbitrary ones and thus now includes, in particular, snap-through instabilities.
KW - Finite time singularity
KW - Free boundary problem
KW - MEMS
UR - http://www.scopus.com/inward/record.url?scp=85045633892&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1612.05761
DO - 10.48550/arXiv.1612.05761
M3 - Article
AN - SCOPUS:85045633892
VL - 37
SP - 209
EP - 219
JO - Zeitschrift fur Analysis und ihre Anwendung
JF - Zeitschrift fur Analysis und ihre Anwendung
SN - 0232-2064
IS - 2
ER -