Details
| Original language | English |
|---|---|
| Pages (from-to) | 134-149 |
| Number of pages | 16 |
| Journal | Communications in Partial Differential Equations |
| Volume | 41 |
| Issue number | 1 |
| Publication status | Published - 4 Jan 2016 |
Abstract
An investigation of qualitative properties of solutions to microelectromechanical systems with nonlinear permittivity profile is established. The considered problem is described by a quasilinear evolution equation for the displacement of a membrane, coupled with an elliptic moving boundary problem for the electrostatic potential between the moving membrane and a rigid ground plate. The system is shown to be well-posed locally in time for arbitrary values λ of the applied voltage. For small values of λ the solution exists even globally in time such that the membrane never touches down on the ground plate. In addition to those fundamental results concerning existence and uniqueness of solutions, sufficient conditions are specified which guarantee non-positivity of the membrane's displacement on the one hand and the occurrence of a singularity after a finite time T on the other hand.
Keywords
- Finite-time singularity, free boundary value problem, general permittivity profile, MEMS, non-positivity
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Communications in Partial Differential Equations, Vol. 41, No. 1, 04.01.2016, p. 134-149.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A qualitative analysis of solutions to microelectromechanical systems with curvature and nonlinear permittivity profile
AU - Escher, Joachim
AU - Lienstromberg, Christina
PY - 2016/1/4
Y1 - 2016/1/4
N2 - An investigation of qualitative properties of solutions to microelectromechanical systems with nonlinear permittivity profile is established. The considered problem is described by a quasilinear evolution equation for the displacement of a membrane, coupled with an elliptic moving boundary problem for the electrostatic potential between the moving membrane and a rigid ground plate. The system is shown to be well-posed locally in time for arbitrary values λ of the applied voltage. For small values of λ the solution exists even globally in time such that the membrane never touches down on the ground plate. In addition to those fundamental results concerning existence and uniqueness of solutions, sufficient conditions are specified which guarantee non-positivity of the membrane's displacement on the one hand and the occurrence of a singularity after a finite time T on the other hand.
AB - An investigation of qualitative properties of solutions to microelectromechanical systems with nonlinear permittivity profile is established. The considered problem is described by a quasilinear evolution equation for the displacement of a membrane, coupled with an elliptic moving boundary problem for the electrostatic potential between the moving membrane and a rigid ground plate. The system is shown to be well-posed locally in time for arbitrary values λ of the applied voltage. For small values of λ the solution exists even globally in time such that the membrane never touches down on the ground plate. In addition to those fundamental results concerning existence and uniqueness of solutions, sufficient conditions are specified which guarantee non-positivity of the membrane's displacement on the one hand and the occurrence of a singularity after a finite time T on the other hand.
KW - Finite-time singularity
KW - free boundary value problem
KW - general permittivity profile
KW - MEMS
KW - non-positivity
UR - http://www.scopus.com/inward/record.url?scp=84953332490&partnerID=8YFLogxK
U2 - 10.1080/03605302.2015.1105259
DO - 10.1080/03605302.2015.1105259
M3 - Article
AN - SCOPUS:84953332490
VL - 41
SP - 134
EP - 149
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
SN - 0360-5302
IS - 1
ER -