论文标题
一般MEMS模型中的达阵解决方案
Touchdown solutions in general MEMS models
论文作者
论文摘要
我们研究通用方程式建模静电mems设备\ begin {equination} \ begin {case} \ label {p}φ\ big（r， - u'（r）\ big）=λ\ int_0^r \ frac {f（s）} {g（u（s）} \，\，\ mathrm {d} s s＆r \ in（in（0,1） 0，\ tag {$p_λ$} \ end {cases} \ end {equation}其中$φ$，$ g $，$ f $是$ [0,1] $上的某些功能，$λ> 0 $是一个参数。我们获得了触地界解决方案对\ eqref {p}的存在和规律性的结果，并在相应的拉力内电压上找到上和下限。在特殊情况下，当$φ（r，v）= r^α| v |^βV$，即，当相关的微分方程涉及操作员$ r^{ - γ}（r^α| u'|^βU'）'$时，我们获得了在启动域中的确切的渐进性行为。
We study general equations modeling electrostatic MEMS devices \begin{equation} \begin{cases} \label{P} φ\big(r,- u'(r)\big)=λ\int_0^r\frac{f(s)}{g(u(s))}\,\mathrm{d}s, & r\in(0,1), \\ 0 < u(r) < 1, & r\in(0,1), \\ u(1) = 0, \tag{$P_λ$} \end{cases} \end{equation} where $φ$, $g$, $f$ are some functions on $[0,1]$ and $λ>0$ is a parameter. We obtain results on the existence and regularity of a touchdown solution to \eqref{P} and find upper and lower bounds on the respective pull-in voltage. In the particular case, when $φ(r,v) = r^α|v|^βv$, i.e., when the associated differential equation involves the operator $r^{-γ}(r^α|u'|^βu')'$, we obtain an exact asymptotic behavior of the touchdown solution in a neighborhood of the origin.
