Comptes Rendus
no. 21-22
Partial differential equations
Finite time singularity in a free boundary problem modeling MEMS
[Singularité en temps fini pour un modèle de microsystème électromécanique à frontière libre]

Présenté par : the Editorial Board

Joachim Escher1 ; Philippe Laurençot2 ; Christoph Walker1
1 Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany
2 Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, 31062 Toulouse cedex 9, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 807-812.

Lʼapparition dʼune singularité en temps fini est établie pour un problème à frontière libre décrivant lʼévolution spatio-temporelle dʼun microsystème électromécanique lorsque la tension appliquée est suffisamment élevée. Le modèle inclut un terme de réaction singulier et un terme non linéaire de courbure, prenant en compte les grandes déformations.

The occurrence of a finite time singularity is shown for a free boundary problem modeling microelectromechanical systems (MEMS) when the applied voltage exceeds some value. The model involves a singular nonlocal reaction term and a nonlinear curvature term taking into account large deformations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.10.004
Joachim Escher 1 ; Philippe Laurençot 2 ; Christoph Walker 1

1 Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany
2 Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, 31062 Toulouse cedex 9, France 
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Joachim Escher; Philippe Laurençot; Christoph Walker. Finite time singularity in a free boundary problem modeling MEMS. Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 807-812. doi : 10.1016/j.crma.2013.10.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.004/

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