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Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties

Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties

Authors :
Katerina Nik
Christoph Walker
Philippe Laurençot
Institut de Mathématiques de Toulouse UMR5219 (IMT)
Université Toulouse Capitole (UT Capitole)
Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)
Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3)
Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Institut für Angewandte Mathematik [Hannover] (IFAM)
Leibniz Universität Hannover=Leibniz University Hannover
Institut für Angewandte Mathematik (IFAM)
Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)
Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Leibniz Universität Hannover [Hannover] (LUH)
Source :
Calculus of variations and partial differential equations 61 (2022), Nr. 1, Calculus of variations and partial differential equations, Calculus of Variations and Partial Differential Equations, Calculus of Variations and Partial Differential Equations, 2022, 61, pp.16
Publication Year :
2020
Publisher :
arXiv, 2020.

Abstract

A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This asymptotic model inherits the dielectric properties of the insulating layer. It involves the electrostatic potential in the device and the deformation of the elastic plate defining the geometry of the device. The electrostatic potential is given by an elliptic equation with mixed boundary conditions in the possibly non-Lipschitz region between the two plates. The deformation of the elastic plate is supposed to be a critical point of an energy functional which, in turn, depends on the electrostatic potential due to the force exerted by the latter on the elastic plate. The energy functional is shown to have a minimizer giving the geometry of the device. Moreover, the corresponding Euler–Lagrange equation is computed and the maximal regularity of the electrostatic potential is established.

Details

ISSN :
09442669 and 14320835
Database :
OpenAIRE
Journal :
Calculus of variations and partial differential equations 61 (2022), Nr. 1, Calculus of variations and partial differential equations, Calculus of Variations and Partial Differential Equations, Calculus of Variations and Partial Differential Equations, 2022, 61, pp.16
Accession number :
edsair.doi.dedup.....3d6eda74db9c04a937d3f80ecf1e2d0e
Full Text :
https://doi.org/10.48550/arxiv.2003.14000