The Time Singular Limit for a Fourth-Order DampedWave Equation for MEMS

被引：3
|
作者：
Laurencot, Philippe [1 ]
Walker, Christoph [2 ]
机构：
[1] Univ Toulouse, Toulouse Inst Math, UMR 5219, CNRS, F-31062 Toulouse 9, France
[2] Leibniz Univ Hannover, Inst Appl Math, D-30167 Hannover, Germany
来源：
ELLIPTIC AND PARABOLIC EQUATIONS | 2015年 / 119卷
关键词：
D O I：
10.1007/978-3-319-12547-3_10
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：233 / 246
页数：14
相关论文
共 50 条
12345