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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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In this paper, we study nonlinear equation arising in MEMS modeling electrostatic actuation. We will prove the local and global existence of solutions of the generalized parabolic MEMS equation. We present that there exists a constant ${\lambda}^*$ such that the associated stationary problem has a solution for any λ < ${\lambda}^*$ and no solution for any λ > ${\lambda}^*$. We show that when λ < ${\lambda}^*$ the global solution converges to its unique maximal steady-state as $t{\rightarrow}{\infty}$. We also obtain the condition for the existence of a touchdown time $T{\leq}{\infty}$ for the dynamical solution. Furthermore, there exists $p_0$ > 1, as a function of $p$, the pull-in voltage ${\lambda}^*(p)$ is strictly decreasing with respect to 1 < $p$ < $p_0$, and increasing with respect to $p$ > $p_0$.
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참고문헌 (13)
참고문헌 신청
A. Friedman / 1964 / Partial Differential Equations of Parabolic Type / Prentice-Hall, Inc.
D. Ye / 2010 / On a general family of nonautonomous elliptic and parabolic equa- tions / Calc. Var. Partial Differential Equations 37 (1) : 259 ~ 274
F. H. Lin / 2007 / Nonlinear non-local elliptic equation modelling electrostatic actuation / Proc. R. Soc. A 463 (2081) : 1323 ~ 1337
G. Flores / 2006 / Analysis of the dynamics and touchdown in a model of electrostatic MEMS / SIAM J. Appl. Math 67 (2) : 434 ~ 446
J. A. Pelesko / 2001 / Mathematical modeling of electrostatic MEMS with tailored dielectric properties / SIAM J. Appl. Math 62 (3) : 888 ~ 908
D. Ye / 2010 / On a general family of nonautonomous elliptic and parabolic equa- tions / Calc. Var. Partial Differential Equations 37 (1) : 259 ~ 274
F. H. Lin / 2007 / Nonlinear non-local elliptic equation modelling electrostatic actuation / Proc. R. Soc. A 463 (2081) : 1323 ~ 1337
G. Flores / 2006 / Analysis of the dynamics and touchdown in a model of electrostatic MEMS / SIAM J. Appl. Math 67 (2) : 434 ~ 446
J. A. Pelesko / 2001 / Mathematical modeling of electrostatic MEMS with tailored dielectric properties / SIAM J. Appl. Math 62 (3) : 888 ~ 908
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