Touchdown is the Only Finite Time Singularity in a Three-Dimensional MEMS Model
Annales mathématiques Blaise Pascal, Volume 27 (2020) no. 1, pp. 65-81.

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.

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.

Published online:
DOI: 10.5802/ambp.391
Classification: 35K91, 35R35, 35M33, 35Q74, 35B44
Keywords: Microelectromechanical system, quenching, free boundary problem, bi-Laplacian
Mot clés : Microsystème électromécanique, désactivation, problème à frontière libre, bi-Laplacien
Philippe Laurençot 1; Christoph Walker 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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Philippe Laurençot; Christoph Walker. Touchdown is the Only Finite Time Singularity in a Three-Dimensional MEMS Model. Annales mathématiques Blaise Pascal, Volume 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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