Details
| Original language | English |
|---|---|
| Pages (from-to) | 437-479 |
| Number of pages | 43 |
| Journal | Bulletin of the American Mathematical Society |
| Volume | 54 |
| Issue number | 3 |
| Publication status | Published - 2017 |
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.
Keywords
- Beam equation, Finite time singularity, Free boundary problem, Microelectromechanical system, Nonlocal nonlinearity, Wave equation, Well-posedness
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Bulletin of the American Mathematical Society, Vol. 54, No. 3, 2017, p. 437-479.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Some singular equations modeling MEMS
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Publisher Copyright: © 2016 American Mathematical Society. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - Beam equation
KW - Finite time singularity
KW - Free boundary problem
KW - Microelectromechanical system
KW - Nonlocal nonlinearity
KW - Wave equation
KW - Well-posedness
UR - http://www.scopus.com/inward/record.url?scp=85020827373&partnerID=8YFLogxK
U2 - 10.1090/bull/1563
DO - 10.1090/bull/1563
M3 - Article
AN - SCOPUS:85020827373
VL - 54
SP - 437
EP - 479
JO - Bulletin of the American Mathematical Society
JF - Bulletin of the American Mathematical Society
SN - 0273-0979
IS - 3
ER -