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Bulletin of the American Mathematical Society

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Some singular equations modeling MEMS


Authors: Philippe Laurençot and Christoph Walker
Journal: Bull. Amer. Math. Soc.
MSC (2010): Primary 35Q74, 35R35, 35M33, 35K91, 35B44, 35B65
DOI: https://doi.org/10.1090/bull/1563
Published electronically: December 28, 2016
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Abstract: In the past fifteen years mathematical models for microelectromechanical systems (MEMS) have been the subject of several studies, in particular due to the interesting qualitative properties they feature. Still most research is devoted to an illustrative but simplified model, which is deduced from a more complex model when the aspect ratio of the device vanishes, the so-called vanishing (or small) aspect ratio model. The analysis of the aforementioned complex model involving a moving boundary has started only recently, and an outlook of the results obtained so far in this direction is provided in this survey.


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Additional Information

Philippe Laurençot
Affiliation: Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, F–31062 Toulouse Cedex 9, France
Email: laurenco@math.univ-toulouse.fr

Christoph Walker
Affiliation: Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, D–30167 Hannover, Germany
Email: walker@ifam.uni-hannover.de

DOI: https://doi.org/10.1090/bull/1563
Keywords: Microelectromechanical system, free boundary problem, nonlocal nonlinearity, finite time singularity, well-posedness, beam equation, wave equation
Received by editor(s): February 21, 2016
Published electronically: December 28, 2016
Additional Notes: Partially supported by the French-German PROCOPE project 30718ZG
Article copyright: © Copyright 2016 American Mathematical Society