
 
Quenching Phenomenon for a Parabolic MEMS Equation 
 
Citation： 
Qi WANG.Quenching Phenomenon for a Parabolic MEMS Equation[J].Chinese Annals of Mathematics B,2018,39(1):129~144 
Page view： 683
Net amount： 268 
Authors： 
Qi WANG; 


Abstract： 
This paper deals with the electrostatic MEMSdevice parabolic
equation
$$u_{t}\Delta u=\d\frac{\lambda f(x)}{(1u)^{p}}$$
in a bounded domain $\O$ of $\r^{N}$, with Dirichlet boundary
condition, an initial condition $u_{0}(x)\in[0,1)$ and a nonnegative
profile $f$, where $\la>0$, $p>1$. The study is motivated by a
simplified microelectromechanical system (MEMS for short) device
model. In this paper, the author first gives an asymptotic behavior
of the quenching time $T^{*}$ for the solution $u$ to the parabolic
problem with zero initial data. Secondly, the author investigates
when the solution $u$ will quench, with general $\la$, $u_{0}(x)$.
Finally, a global existence in the MEMS modeling is shown. 
Keywords： 
MEMS equation, Quenching time, Global existence 
Classification： 
35A01, 35B44, 35K58 

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