Communications in Mathematical Sciences
Volume 13 (2015)
Asymptotic stability and quenching behavior of a hyperbolic nonlocal MEMS equation
Pages: 355 – 368
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.
micro-electro-mechanical system, nonlocal, wave equation, global existence, asymptotic stability
2010 Mathematics Subject Classification
34B10, 35A01, 35B40, 35L05, 93D20