A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid ground plate. The model couples a non-local fourth-order equation for the elastic plate deflection to the harmonic electrostatic potential in the free domain between the elastic and the ground plate. The corresponding energy is non-coercive reflecting an inherent singularity related to a possible touchdown of the elastic plate. Stationary solutions are constructed using a constrained minimization problem. A by-product is the existence of at least two stationary solutions for some values of the applied voltage.
DOI : 10.1051/cocv/2015012
Mots clés : MEMS, free boundary, stationary solutions, multiplicity, constrained minimization
@article{COCV_2016__22_2_417_0,
author = {Lauren\c{c}ot, Philippe and Walker, Christoph},
title = {A variational approach to a stationary free boundary problem modeling {MEMS}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {417--438},
publisher = {EDP-Sciences},
volume = {22},
number = {2},
year = {2016},
doi = {10.1051/cocv/2015012},
mrnumber = {3491777},
zbl = {1341.35038},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2015012/}
}
TY - JOUR AU - Laurençot, Philippe AU - Walker, Christoph TI - A variational approach to a stationary free boundary problem modeling MEMS JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 417 EP - 438 VL - 22 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2015012/ DO - 10.1051/cocv/2015012 LA - en ID - COCV_2016__22_2_417_0 ER -
%0 Journal Article %A Laurençot, Philippe %A Walker, Christoph %T A variational approach to a stationary free boundary problem modeling MEMS %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 417-438 %V 22 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2015012/ %R 10.1051/cocv/2015012 %G en %F COCV_2016__22_2_417_0
Laurençot, Philippe; Walker, Christoph. A variational approach to a stationary free boundary problem modeling MEMS. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 417-438. doi : 10.1051/cocv/2015012. http://www.numdam.org/articles/10.1051/cocv/2015012/
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