Details
| Original language | English |
|---|---|
| Pages (from-to) | 307-349 |
| Number of pages | 43 |
| Journal | Mathematische Annalen |
| Volume | 360 |
| Issue number | 1-2 |
| Publication status | Published - 7 Sept 2014 |
Abstract
The dynamical and stationary behaviors of a fourth-order evolution equation with clamped boundary conditions and a singular nonlocal reaction term, which is coupled to an elliptic free boundary problem in a non-smooth domain, are investigated. The equation arises in the modeling of microelectromechanical systems and includes two positive parameters (formula presented) and (formula presented) related to the applied voltage and the aspect ratio of the device, respectively. Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as a criterion for global existence excluding the occurrence of finite time singularities which are not physically relevant. Existence of a stable steady state is shown for sufficiently small (formula presented). Non-existence of steady states is also established when (formula presented) is small enough and (formula presented) is large enough (depending on (formula presented).
Keywords
- 35B60, 35K91, 35M33, 35Q74, 35R35
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Annalen, Vol. 360, No. 1-2, 07.09.2014, p. 307-349.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A free boundary problem modeling electrostatic MEMS
T2 - I. Linear bending effects
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Funding information: The work of Ph.L. was partially supported by the CIMI (Centre International de Mathématiques et d’Informatique) Excellence program and by the Deutscher Akademischer Austausch Dienst (DAAD) while enjoying the hospitality of the Institut für Angewandte Mathematik, Leibniz Universität Hannover. Partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02.
PY - 2014/9/7
Y1 - 2014/9/7
N2 - The dynamical and stationary behaviors of a fourth-order evolution equation with clamped boundary conditions and a singular nonlocal reaction term, which is coupled to an elliptic free boundary problem in a non-smooth domain, are investigated. The equation arises in the modeling of microelectromechanical systems and includes two positive parameters (formula presented) and (formula presented) related to the applied voltage and the aspect ratio of the device, respectively. Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as a criterion for global existence excluding the occurrence of finite time singularities which are not physically relevant. Existence of a stable steady state is shown for sufficiently small (formula presented). Non-existence of steady states is also established when (formula presented) is small enough and (formula presented) is large enough (depending on (formula presented).
AB - The dynamical and stationary behaviors of a fourth-order evolution equation with clamped boundary conditions and a singular nonlocal reaction term, which is coupled to an elliptic free boundary problem in a non-smooth domain, are investigated. The equation arises in the modeling of microelectromechanical systems and includes two positive parameters (formula presented) and (formula presented) related to the applied voltage and the aspect ratio of the device, respectively. Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as a criterion for global existence excluding the occurrence of finite time singularities which are not physically relevant. Existence of a stable steady state is shown for sufficiently small (formula presented). Non-existence of steady states is also established when (formula presented) is small enough and (formula presented) is large enough (depending on (formula presented).
KW - 35B60
KW - 35K91
KW - 35M33
KW - 35Q74
KW - 35R35
UR - http://www.scopus.com/inward/record.url?scp=84919875774&partnerID=8YFLogxK
U2 - 10.1007/s00208-014-1032-8
DO - 10.1007/s00208-014-1032-8
M3 - Article
AN - SCOPUS:84919875774
VL - 360
SP - 307
EP - 349
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 1-2
ER -