Display Abstract

Title On a hyperbolic equation in MEMS

Name Jingyu Li
Country Peoples Rep of China
Email lijy645@nenu.edu.cn
Co-Author(s) Chuangchuang Liang and Kaijun Zhang
Submit Time 2014-02-25 19:12:24
Special Session 37: Global or/and blowup solutions for nonlinear evolution equations and their applications
We consider a damped wave equation with singular nonlinearity and Dirichlet boundary condition in a bounded domain, which describes an electrostatic micro-electro-mechanical system (MEMS) device. We show that the pull-in voltage $\lambda^*$ is the critical threshold for global existence and quenching in this wave equation. More precisely, if the applied voltage $\lambda\lambda^*$, then any solution quenches in finite time. Finally, we analyze the relation between the hyperbolic model and the parabolic model through the viscosity dominated limit.