MATHEMATICAL ANALYSIS OF NONLINEAR DIFFERENTIAL EQUATION ARISING IN MEMS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 49, Issue 4, 2012, pp.705-714
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2012.49.4.705

Title & Authors

MATHEMATICAL ANALYSIS OF NONLINEAR DIFFERENTIAL EQUATION ARISING IN MEMS

Zhang, Ruifeng; Li, Na;

Zhang, Ruifeng; Li, Na;

Abstract

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 such that the associated stationary problem has a solution for any < and no solution for any > . We show that when < the global solution converges to its unique maximal steady-state as . We also obtain the condition for the existence of a touchdown time for the dynamical solution. Furthermore, there exists > 1, as a function of , the pull-in voltage is strictly decreasing with respect to 1 < < , and increasing with respect to > .

Keywords

MEMS equation;upper-and-lower solution method;global convergence;touchdown time;

Language

English

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