Details
| Translated title of the contribution | Touchdown is the only finite time singularity in a three-dimensional mems model |
|---|---|
| Original language | French |
| Pages (from-to) | 65-81 |
| Number of pages | 17 |
| Journal | Annales Mathematiques Blaise Pascal |
| Volume | 27 |
| Issue number | 1 |
| Early online date | 26 Aug 2020 |
| Publication status | Published - 26 Aug 2020 |
Abstract
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 L1 by the bi-Laplacian with clamped boundary conditions.
Keywords
- Bi-Laplacian, Free boundary problem, Microelectromechanical system, Quenching
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Geometry and Topology
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In: Annales Mathematiques Blaise Pascal, Vol. 27, No. 1, 26.08.2020, p. 65-81.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - La désactivation est la seule singularité en temps fini possible dans un modèle de mems tridimensionnel
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Funding information: Partially supported by the CNRS Projet International de Coopération Scientifique PICS07710. Keywords: Microelectromechanical system, quenching, free boundary problem, bi-Laplacian. 2020 Mathematics Subject Classification: 35K91, 35R35, 35M33, 35Q74, 35B44.
PY - 2020/8/26
Y1 - 2020/8/26
N2 - 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 L1 by the bi-Laplacian with clamped boundary conditions.
AB - 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 L1 by the bi-Laplacian with clamped boundary conditions.
KW - Bi-Laplacian
KW - Free boundary problem
KW - Microelectromechanical system
KW - Quenching
UR - http://www.scopus.com/inward/record.url?scp=85091633329&partnerID=8YFLogxK
U2 - 10.5802/ambp.391
DO - 10.5802/ambp.391
M3 - Article
AN - SCOPUS:85091633329
VL - 27
SP - 65
EP - 81
JO - Annales Mathematiques Blaise Pascal
JF - Annales Mathematiques Blaise Pascal
SN - 1259-1734
IS - 1
ER -