SOME SINGULAR EQUATIONS MODELING MEMS

被引：33
作者：
Laurencot, Philippe [1 ]
Walker, Christoph [2 ]
机构：
[1] Univ Toulouse, Inst Math Toulouse, UMR 5219, CNRS, F-31062 Toulouse 9, France
[2] Leibniz Univ Hannover, Inst Angew Math, Welfengarten 1, D-30167 Hannover, Germany
来源：
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 54卷 / 03期
关键词：
Microelectromechanical system; free boundary problem; nonlocal nonlinearity; finite time singularity; well-posedness; beam equation; wave equation; FREE-BOUNDARY PROBLEM; PARTIAL-DIFFERENTIAL-EQUATIONS; POST-TOUCHDOWN CONFIGURATIONS; NONLINEAR EIGENVALUE PROBLEMS; NONLOCAL PARABOLIC PROBLEM; MEAN-CURVATURE EQUATION; PULL-IN INSTABILITY; VAN-DER-WAALS; ELECTROSTATIC MEMS; QUENCHING BEHAVIOR;
D O I：
10.1090/bull/1563
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：437 / 479
页数：43
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