Touchdown is the Only Finite Time Singularity in a Three-Dimensional MEMS Model
[La désactivation est la seule singularité en temps fini possible dans un modèle de MEMS tridimensionnel]
Annales Mathématiques Blaise Pascal, Tome 27 (2020) no. 1, pp. 65-81.

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 L 1 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 L 1 by the bi-Laplacian with clamped boundary conditions.

Publié le :
DOI : https://doi.org/10.5802/ambp.391
Classification : 35K91,  35R35,  35M33,  35Q74,  35B44
Mots clés : Microsystème électromécanique, désactivation, problème à frontière libre, bi-Laplacien
@article{AMBP_2020__27_1_65_0,
     author = {Philippe Lauren\c{c}ot and Christoph Walker},
     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 = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.391/}
}
Philippe Laurençot; Christoph Walker. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.391/

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