Details
| Original language | English |
|---|---|
| Pages (from-to) | 1435-1464 |
| Number of pages | 30 |
| Journal | Proceedings of the London Mathematical Society |
| Volume | 109 |
| Issue number | 6 |
| Publication status | Published - 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 subject areas
- Mathematics(all)
- General Mathematics
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In: Proceedings of the London Mathematical Society, Vol. 109, No. 6, 23.08.2013, p. 1435-1464.
Research output: Contribution to journal › Article › Research › 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 -