Details
| Original language | English |
|---|---|
| Pages (from-to) | 1961-1976 |
| Number of pages | 16 |
| Journal | Annali di Matematica Pura ed Applicata |
| Volume | 195 |
| Issue number | 6 |
| Publication status | Published - 21 Jan 2016 |
Abstract
Of concern is a study of qualitative properties of solutions to the evolution problem modelling microelectromechanical systems with general permittivity. The system couples a quasilinear parabolic evolution problem for a membrane’s displacement with an elliptic free boundary value problem for the electrostatic potential in the region between the membrane and a rigid ground plate. It is shown that, under a structural condition on the permittivity profile, non-positive solutions develop a singularity in finite time, provided that the applied voltage is large enough and the aspect ratio of the system is small enough.
Keywords
- Finite-time singularity, Free boundary value problem, General permittivity profile, MEMS
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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In: Annali di Matematica Pura ed Applicata, Vol. 195, No. 6, 21.01.2016, p. 1961-1976.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Finite-Time Singularities of Solutions to Microelectromechanical Systems with General Permittivity
AU - Escher, Joachim
AU - Lienstromberg, Christina
PY - 2016/1/21
Y1 - 2016/1/21
N2 - Of concern is a study of qualitative properties of solutions to the evolution problem modelling microelectromechanical systems with general permittivity. The system couples a quasilinear parabolic evolution problem for a membrane’s displacement with an elliptic free boundary value problem for the electrostatic potential in the region between the membrane and a rigid ground plate. It is shown that, under a structural condition on the permittivity profile, non-positive solutions develop a singularity in finite time, provided that the applied voltage is large enough and the aspect ratio of the system is small enough.
AB - Of concern is a study of qualitative properties of solutions to the evolution problem modelling microelectromechanical systems with general permittivity. The system couples a quasilinear parabolic evolution problem for a membrane’s displacement with an elliptic free boundary value problem for the electrostatic potential in the region between the membrane and a rigid ground plate. It is shown that, under a structural condition on the permittivity profile, non-positive solutions develop a singularity in finite time, provided that the applied voltage is large enough and the aspect ratio of the system is small enough.
KW - Finite-time singularity
KW - Free boundary value problem
KW - General permittivity profile
KW - MEMS
UR - http://www.scopus.com/inward/record.url?scp=84955264792&partnerID=8YFLogxK
U2 - 10.1007/s10231-016-0549-8
DO - 10.1007/s10231-016-0549-8
M3 - Article
AN - SCOPUS:84955264792
VL - 195
SP - 1961
EP - 1976
JO - Annali di Matematica Pura ed Applicata
JF - Annali di Matematica Pura ed Applicata
SN - 0373-3114
IS - 6
ER -