"Subject of consideration is the analytical investigation of a coupled system of partial differential equations arising from the modelling of electrostatically actuated microelectromechanical systems with general permittivity profile. A quasilinear parabolic evolution problem for the displacement u of an elastic membrane is coupled with an elliptic free boundary value problem that determines the electrostatic potential ψ in the region between the elastic membrane and a rigid ground plate. The system is shown to be well-posed locally in time for all arbitrarily large values λ of the applied voltage, whereas small values of the applied voltage, which do not exceed a certain critical value λ∗, do even allow globally in time existing solutions. In addition, conditions are specified which force solutions emerging from a non-positive initial deflection to stay non-positive as long as they exist.''
%0 Journal Article
%1 MR3722055
%A Lienstromberg, Christina
%D 2017
%J J. Evol. Equ.
%K Lienstromberg IADM problem from:elkepeter MEMS evolution quasilinear modelling
%N 4
%P 1129--1150
%R 10.1007/s00028-016-0375-x
%T Well-posedness of a quasilinear evolution problem modelling
MEMS with general permittivity
%U https://doi.org/10.1007/s00028-016-0375-x
%V 17
%X "Subject of consideration is the analytical investigation of a coupled system of partial differential equations arising from the modelling of electrostatically actuated microelectromechanical systems with general permittivity profile. A quasilinear parabolic evolution problem for the displacement u of an elastic membrane is coupled with an elliptic free boundary value problem that determines the electrostatic potential ψ in the region between the elastic membrane and a rigid ground plate. The system is shown to be well-posed locally in time for all arbitrarily large values λ of the applied voltage, whereas small values of the applied voltage, which do not exceed a certain critical value λ∗, do even allow globally in time existing solutions. In addition, conditions are specified which force solutions emerging from a non-positive initial deflection to stay non-positive as long as they exist.''
@article{MR3722055,
abstract = {"Subject of consideration is the analytical investigation of a coupled system of partial differential equations arising from the modelling of electrostatically actuated microelectromechanical systems with general permittivity profile. A quasilinear parabolic evolution problem for the displacement u of an elastic membrane is coupled with an elliptic free boundary value problem that determines the electrostatic potential ψ in the region between the elastic membrane and a rigid ground plate. The system is shown to be well-posed locally in time for all arbitrarily large values λ of the applied voltage, whereas small values of the applied voltage, which do not exceed a certain critical value λ∗, do even allow globally in time existing solutions. In addition, conditions are specified which force solutions emerging from a non-positive initial deflection to stay non-positive as long as they exist.''},
added-at = {2023-03-27T11:18:04.000+0200},
author = {Lienstromberg, Christina},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/215cbaa595a6eb4993ab86ab418376c26/mathematik},
doi = {10.1007/s00028-016-0375-x},
fjournal = {Journal of Evolution Equations},
interhash = {64986724c4398d14ae2c3ea8f153a653},
intrahash = {15cbaa595a6eb4993ab86ab418376c26},
issn = {1424-3199},
journal = {J. Evol. Equ.},
keywords = {Lienstromberg IADM problem from:elkepeter MEMS evolution quasilinear modelling},
mrclass = {35K59 (35B09 35B30 35B44 35K20 35R35 74M05)},
mrnumber = {3722055},
number = 4,
pages = {1129--1150},
timestamp = {2023-12-05T17:17:36.000+0100},
title = {Well-posedness of a quasilinear evolution problem modelling
{MEMS} with general permittivity},
url = {https://doi.org/10.1007/s00028-016-0375-x},
volume = 17,
year = 2017
}
