Some singular equations modeling MEMS
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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.References
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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
- MR Author ID: 695761
- Email: walker@ifam.uni-hannover.de
- Received by editor(s): February 21, 2016
- Published electronically: December 28, 2016
- Additional Notes: Partially supported by the French-German PROCOPE project 30718ZG
- © Copyright 2016 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 54 (2017), 437-479
- MSC (2010): Primary 35Q74, 35R35, 35M33, 35K91, 35B44, 35B65
- DOI: https://doi.org/10.1090/bull/1563
- MathSciNet review: 3662914