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| Quenching Phenomenon for a Parabolic MEMS Equation |
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Citation： |
Qi WANG.Quenching Phenomenon for a Parabolic MEMS Equation[J].Chinese Annals of Mathematics B,2018,39(1):129~144 |
| Page view： 1811
Net amount： 1159 |
Authors： |
Qi WANG; |
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| Abstract： |
This paper deals with the electrostatic MEMS-device parabolic
equation
$$u_{t}-\Delta u=\d\frac{\lambda f(x)}{(1-u)^{p}}$$
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 micro-electromechanical 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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