Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1435-1464 |
| Seitenumfang | 30 |
| Fachzeitschrift | Proceedings of the London Mathematical Society |
| Jahrgang | 109 |
| Ausgabenummer | 6 |
| Publikationsstatus | Veröffentlicht - 23 Aug. 2013 |
Abstract
The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems and includes a positive voltage parameter λ. It is shown that there is a threshold value λ∗ >0 of the voltage parameter such that no radially symmetric stationary solution exists for λ >λ∗, while at least two such solutions exist for λ ε (0,λ∗). Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as the occurrence of finite time singularities when λ > λ∗.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Proceedings of the London Mathematical Society, Jahrgang 109, Nr. 6, 23.08.2013, S. 1435-1464.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - A fourth-order model for MEMS with clamped boundary conditions
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Funding information: This research was partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02. The work of Ph. L. was partially supported by the CIMI (Centre International de Mathématiques et d’Informatique) Excellence program.
PY - 2013/8/23
Y1 - 2013/8/23
N2 - The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems and includes a positive voltage parameter λ. It is shown that there is a threshold value λ∗ >0 of the voltage parameter such that no radially symmetric stationary solution exists for λ >λ∗, while at least two such solutions exist for λ ε (0,λ∗). Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as the occurrence of finite time singularities when λ > λ∗.
AB - The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems and includes a positive voltage parameter λ. It is shown that there is a threshold value λ∗ >0 of the voltage parameter such that no radially symmetric stationary solution exists for λ >λ∗, while at least two such solutions exist for λ ε (0,λ∗). Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as the occurrence of finite time singularities when λ > λ∗.
UR - http://www.scopus.com/inward/record.url?scp=84928896589&partnerID=8YFLogxK
U2 - 10.1112/plms/pdu037
DO - 10.1112/plms/pdu037
M3 - Article
AN - SCOPUS:84928896589
VL - 109
SP - 1435
EP - 1464
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
SN - 0024-6115
IS - 6
ER -