Communications in Mathematical Sciences

Volume 13 (2015)

Number 2

Asymptotic stability and quenching behavior of a hyperbolic nonlocal MEMS equation

Pages: 355 – 368

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n2.a5

Authors

Chuangchuang Liang (School of Mathematics and Statistics, Northeast Normal University, Changchun, China; and School of Mathematical Sciences, Capital Normal University, Beijing, China)

Kaijun Zhang (School of Mathematics and Statistics, Northeast Normal University, Changchun, China)

Abstract

We investigate a nonlocal wave equation with damping term and singular nonlinearity, which models an electrostatic micro-electro-mechanical system (MEMS) device. In the case of the relative strength parameter $\lambda$ being small, the existence and uniqueness of the global solution are established. Moreover, the asymptotic result that the solution exponentially converges to the steady state solution is also proved. For large $\lambda$, quenching results of the solution are obtained.

Keywords

micro-electro-mechanical system, nonlocal, wave equation, global existence, asymptotic stability

2010 Mathematics Subject Classification

34B10, 35A01, 35B40, 35L05, 93D20

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Published 3 December 2014