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The Time Singular Limit for a Fourth-Order Damped Wave Equation for MEMS

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Elliptic and Parabolic Equations

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 119))

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Abstract

We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential. We first review some recent results on existence and nonexistence of steady states as well as on local and global well-posedness of the dynamical problem, the main focus being on the possible touchdown behavior of the elastic plate. We then investigate the behavior of the solutions in the time singular limit, when the ratio between inertial and damping effects decays to zero.

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Author information

Authors and Affiliations

  1. Toulouse Institute of Mathematics, UMR 5219, University of Toulouse, CNRS, 31062, Toulouse Cedex 9, France

    Philippe Laurençot

  2. Institute for Applied Mathematics, Leibniz University of Hannover, 30167, Hannover, Germany

    Christoph Walker

Authors
  1. Philippe Laurençot
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  2. Christoph Walker
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Corresponding author

Correspondence to Philippe Laurençot .

Editor information

Editors and Affiliations

  1. Institute for Applied Mathematics, Leibniz University of Hannover, Hannover, Germany

    Joachim Escher

  2. Institute for Analysis, Leibniz University of Hannover, Hannover, Germany

    Elmar Schrohe

  3. Department of Mathematics, University of Torino, Torino, Torino, Italy

    Jörg Seiler

  4. Institute for Applied Mathematics, Leibniz University of Hannover, Hannover, Germany

    Christoph Walker

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Laurençot, P., Walker, C. (2015). The Time Singular Limit for a Fourth-Order Damped Wave Equation for MEMS. In: Escher, J., Schrohe, E., Seiler, J., Walker, C. (eds) Elliptic and Parabolic Equations. Springer Proceedings in Mathematics & Statistics, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-12547-3_10

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