[La désactivation est la seule singularité en temps fini possible dans un modèle de MEMS tridimensionnel]
Nous montrons que la désactivation est la seule singularité en temps fini pouvant se produire dans un problème à frontière libre décrivant un microsystème électromécanique tridimensionnel. La démonstration repose sur la structure variationnelle du modèle et utilise les propriétés régularisantes du semi-groupe engendré dans par le bi-Laplacien avec conditions aux bords encastrées.
Touchdown is shown to be the only possible finite time singularity that may take place in a free boundary problem modeling a three-dimensional microelectromechanical system. The proof relies on the energy structure of the problem and uses smoothing effects of the semigroup generated in by the bi-Laplacian with clamped boundary conditions.
Keywords: Microelectromechanical system, quenching, free boundary problem, bi-Laplacian
Mot clés : Microsystème électromécanique, désactivation, problème à frontière libre, bi-Laplacien
@article{AMBP_2020__27_1_65_0,
author = {Lauren\c{c}ot, Philippe and Walker, Christoph},
title = {Touchdown is the {Only} {Finite} {Time} {Singularity} in a {Three-Dimensional} {MEMS} {Model}},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {65--81},
publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
volume = {27},
number = {1},
year = {2020},
doi = {10.5802/ambp.391},
language = {en},
url = {http://www.numdam.org/articles/10.5802/ambp.391/}
}
TY - JOUR AU - Laurençot, Philippe AU - Walker, Christoph TI - Touchdown is the Only Finite Time Singularity in a Three-Dimensional MEMS Model JO - Annales mathématiques Blaise Pascal PY - 2020 SP - 65 EP - 81 VL - 27 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.391/ DO - 10.5802/ambp.391 LA - en ID - AMBP_2020__27_1_65_0 ER -
%0 Journal Article %A Laurençot, Philippe %A Walker, Christoph %T Touchdown is the Only Finite Time Singularity in a Three-Dimensional MEMS Model %J Annales mathématiques Blaise Pascal %D 2020 %P 65-81 %V 27 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.391/ %R 10.5802/ambp.391 %G en %F AMBP_2020__27_1_65_0
Laurençot, Philippe; Walker, Christoph. Touchdown is the Only Finite Time Singularity in a Three-Dimensional MEMS Model. Annales mathématiques Blaise Pascal, Tome 27 (2020) no. 1, pp. 65-81. doi : 10.5802/ambp.391. http://www.numdam.org/articles/10.5802/ambp.391/
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