dc.identifier.uri |
http://dx.doi.org/10.15488/2333 |
|
dc.identifier.uri |
http://www.repo.uni-hannover.de/handle/123456789/2359 |
|
dc.contributor.author |
Laurençot, P.
|
|
dc.contributor.author |
Walker, C.
|
|
dc.date.accessioned |
2017-11-17T09:49:38Z |
|
dc.date.available |
2017-11-17T09:49:38Z |
|
dc.date.issued |
2016 |
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dc.identifier.citation |
Laurençot, P.; Walker, C.: On a three-dimensional free boundary problem modeling electrostatic MEMS. In: Interfaces and Free Boundaries 18 (2016), Nr. 3, S. 393-411. DOI: https://doi.org/10.4171/IFB/368 |
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dc.description.abstract |
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 λ 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 λ solutions exist globally in time. We also derive the existence of a branch of asymptotically stable stationary solutions for small values of λ and non-existence of stationary solutions for large values thereof, the latter being restricted to a disc-shaped plate. © European Mathematical Society 2016. |
eng |
dc.language.iso |
eng |
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dc.publisher |
Zürich : European Mathematical Society Publishing House |
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dc.relation.ispartofseries |
Interfaces and Free Boundaries 18 (2016), Nr. 3 |
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dc.rights |
Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. |
|
dc.subject |
Free boundary problem |
eng |
dc.subject |
MEMS |
eng |
dc.subject |
Stationary solutions |
eng |
dc.subject.ddc |
510 | Mathematik
|
ger |
dc.title |
On a three-dimensional free boundary problem modeling electrostatic MEMS |
|
dc.type |
Article |
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dc.type |
Text |
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dc.relation.issn |
1463-9963 |
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dc.relation.doi |
https://doi.org/10.4171/IFB/368 |
|
dc.bibliographicCitation.issue |
3 |
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dc.bibliographicCitation.volume |
18 |
|
dc.bibliographicCitation.firstPage |
393 |
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dc.bibliographicCitation.lastPage |
411 |
|
dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
|