Details
| Original language | English |
|---|---|
| Title of host publication | Elliptic and Parabolic Equations |
| Subtitle of host publication | Hannover, September 2013 |
| Editors | Joachim Escher, Elmar Schrohe, Jörg Seiler, Christoph Walker |
| Pages | 233-246 |
| Number of pages | 14 |
| ISBN (electronic) | 978-3-319-12547-3 |
| Publication status | Published - 5 Jun 2015 |
| Event | International Workshop on Elliptic and Parabolic Equations, 2013 - Hannover, Germany Duration: 10 Sept 2013 → 12 Sept 2013 |
Publication series
| Name | Springer Proceedings in Mathematics and Statistics |
|---|---|
| Publisher | Springer Publishing Company |
| Volume | 119 |
| ISSN (Print) | 2194-1009 |
| ISSN (electronic) | 2194-1017 |
Abstract
We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential.We first review some recent results on existence and nonexistence of steady states as well as on local and global well-posedness of the dynamical problem, the main focus being on the possible touchdown behavior of the elastic plate. We then investigate the behavior of the solutions in the time singular limit, when the ratio between inertial and damping effects decays to zero.
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Elliptic and Parabolic Equations: Hannover, September 2013. ed. / Joachim Escher; Elmar Schrohe; Jörg Seiler; Christoph Walker. 2015. p. 233-246 (Springer Proceedings in Mathematics and Statistics; Vol. 119).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - The Time Singular Limit for a Fourth-Order Damped Wave Equation for MEMS
AU - Laurençot, Philippe
AU - Walker, Christoph
PY - 2015/6/5
Y1 - 2015/6/5
N2 - We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential.We first review some recent results on existence and nonexistence of steady states as well as on local and global well-posedness of the dynamical problem, the main focus being on the possible touchdown behavior of the elastic plate. We then investigate the behavior of the solutions in the time singular limit, when the ratio between inertial and damping effects decays to zero.
AB - We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential.We first review some recent results on existence and nonexistence of steady states as well as on local and global well-posedness of the dynamical problem, the main focus being on the possible touchdown behavior of the elastic plate. We then investigate the behavior of the solutions in the time singular limit, when the ratio between inertial and damping effects decays to zero.
KW - math.AP
UR - http://www.scopus.com/inward/record.url?scp=84931435358&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1404.6342
DO - 10.48550/arXiv.1404.6342
M3 - Conference contribution
AN - SCOPUS:84931435358
SN - 978-3-319-12546-6
SN - 978-3-319-38150-3
T3 - Springer Proceedings in Mathematics and Statistics
SP - 233
EP - 246
BT - Elliptic and Parabolic Equations
A2 - Escher, Joachim
A2 - Schrohe, Elmar
A2 - Seiler, Jörg
A2 - Walker, Christoph
T2 - International Workshop on Elliptic and Parabolic Equations, 2013
Y2 - 10 September 2013 through 12 September 2013
ER -