Open AccessUpper and lower bounds for the pull-in voltage and the pull-in distance for a generalized MEMS problem
Author(s) -
Yan-Hsiou Cheng,
KuoChih Hung,
ShinHwa Wang,
Jhih-Jyun Zeng
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022321
Subject(s) - lambda , prime (order theory) , monotonic function , combinatorics , mathematics , curvature , upper and lower bounds , voltage , physics , mathematical analysis , geometry , quantum mechanics
We study upper and lower bounds for the pull-in voltage and the pull-in distance for the one-dimensional prescribed mean curvature problem arising in MEMS $ \begin{equation*} \left \{\begin{array}{l} - \left( \frac{u^{ \prime } (x)}{\sqrt{1 +\left (u^{ \prime } (x)\right )^{2}}} \right)^{ \prime } = \frac{\lambda }{(1 -u)^{p}} , \ \ u <1 , \ \ -L <x <L, \\ u ( -L) = u (L) = 0, \end{array}\right . \end{equation*} $ where $ \lambda > 0 $ is a bifurcation parameter, and $ p, L > 0 $ are two evolution parameters. We further study monotonicity properties and asymptotic behaviors for the pull-in voltage and pull-in distance with respect to positive parameters $ p $ and $ L $.