Geodesic
A variational approach to a stationary free boundary problem modeling MEMS
Laurençot, Philippe1  ; Walker, Christoph2 
1 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, 31062 Toulouse cedex 9, France.
2 Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 417-438 Cet article a éte moissonné depuis la source Numdam

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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.

Reçu le :
DOI : 10.1051/cocv/2015012
Classification : 35J35, 35R35, 35Q74
Keywords: MEMS, free boundary, stationary solutions, multiplicity, constrained minimization

Laurençot, Philippe 1 ; Walker, Christoph 2

1 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, 31062 Toulouse cedex 9, France.
2 Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany. 
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     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},
     year = {2016},
     publisher = {EDP-Sciences},
     volume = {22},
     number = {2},
     doi = {10.1051/cocv/2015012},
     mrnumber = {3491777},
     zbl = {1341.35038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015012/}
}
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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

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