Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 15-51 |
| Seitenumfang | 37 |
| Fachzeitschrift | Journal of Elliptic and Parabolic Equations |
| Jahrgang | 3 |
| Ausgabenummer | 1-2 |
| Publikationsstatus | Veröffentlicht - 1 Dez. 2017 |
Abstract
A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential threshold is not accompanied by a break-down of the model, but is recovered by the saturation of the constraint for pulled-in states. It is shown that a maximal stationary solution exists and that saturation only occurs for large potential values. In addition, the existence, uniqueness, and large time behavior of solutions to the evolution equation are studied.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
- Mathematik (insg.)
- Numerische Mathematik
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in: Journal of Elliptic and Parabolic Equations, Jahrgang 3, Nr. 1-2, 01.12.2017, S. 15-51.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - A constrained model for MEMS with varying dielectric properties
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Funding information: Part of this work was done while PhL enjoyed the hospitality and support of the Institut für Angewandte Mathematik, Leibniz Universität Hannover.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential threshold is not accompanied by a break-down of the model, but is recovered by the saturation of the constraint for pulled-in states. It is shown that a maximal stationary solution exists and that saturation only occurs for large potential values. In addition, the existence, uniqueness, and large time behavior of solutions to the evolution equation are studied.
AB - A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential threshold is not accompanied by a break-down of the model, but is recovered by the saturation of the constraint for pulled-in states. It is shown that a maximal stationary solution exists and that saturation only occurs for large potential values. In addition, the existence, uniqueness, and large time behavior of solutions to the evolution equation are studied.
KW - Large time behavior
KW - MEMS
KW - Obstacle problem
KW - Parabolic variational inequality
KW - Well-posedness
UR - http://www.scopus.com/inward/record.url?scp=85043763847&partnerID=8YFLogxK
U2 - 10.1007/s41808-017-0003-0
DO - 10.1007/s41808-017-0003-0
M3 - Article
AN - SCOPUS:85043763847
VL - 3
SP - 15
EP - 51
JO - Journal of Elliptic and Parabolic Equations
JF - Journal of Elliptic and Parabolic Equations
SN - 2296-9020
IS - 1-2
ER -