A constrained model for MEMS with varying dielectric properties

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Philippe Laurençot
  • Christoph Walker

Research Organisations

External Research Organisations

  • Universite de Toulouse
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Details

Original languageEnglish
Pages (from-to)15-51
Number of pages37
JournalJournal of Elliptic and Parabolic Equations
Volume3
Issue number1-2
Publication statusPublished - 1 Dec 2017

Abstract

A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential threshold is not accompanied by a break-down of the model, but is recovered by the saturation of the constraint for pulled-in states. It is shown that a maximal stationary solution exists and that saturation only occurs for large potential values. In addition, the existence, uniqueness, and large time behavior of solutions to the evolution equation are studied.

Keywords

    Large time behavior, MEMS, Obstacle problem, Parabolic variational inequality, Well-posedness

ASJC Scopus subject areas

Cite this

A constrained model for MEMS with varying dielectric properties. / Laurençot, Philippe; Walker, Christoph.
In: Journal of Elliptic and Parabolic Equations, Vol. 3, No. 1-2, 01.12.2017, p. 15-51.

Research output: Contribution to journal › Article › Research › peer review

Laurençot, P & Walker, C 2017, 'A constrained model for MEMS with varying dielectric properties', Journal of Elliptic and Parabolic Equations, vol. 3, no. 1-2, pp. 15-51. https://doi.org/10.1007/s41808-017-0003-0
Laurençot, P., & Walker, C. (2017). A constrained model for MEMS with varying dielectric properties. Journal of Elliptic and Parabolic Equations, 3(1-2), 15-51. https://doi.org/10.1007/s41808-017-0003-0
Laurençot P, Walker C. A constrained model for MEMS with varying dielectric properties. Journal of Elliptic and Parabolic Equations. 2017 Dec 1;3(1-2):15-51. doi: 10.1007/s41808-017-0003-0
Laurençot, Philippe ; Walker, Christoph. / A constrained model for MEMS with varying dielectric properties. In: Journal of Elliptic and Parabolic Equations. 2017 ; Vol. 3, No. 1-2. pp. 15-51.
Download
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AU - Walker, Christoph

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N2 - A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential threshold is not accompanied by a break-down of the model, but is recovered by the saturation of the constraint for pulled-in states. It is shown that a maximal stationary solution exists and that saturation only occurs for large potential values. In addition, the existence, uniqueness, and large time behavior of solutions to the evolution equation are studied.

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KW - Obstacle problem

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KW - Well-posedness

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