MATHEMATICAL ANALYSIS OF NONLINEAR DIFFERENTIAL EQUATION ARISING IN MEMS

Ruifeng Zhang, Na Li
2012 Bulletin of the Korean Mathematical Society  
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 λ * such that the associated stationary problem has a solution for any λ < λ * and no solution for any λ > λ * . We show that when λ < λ * the global solution converges to its unique maximal steady-state as t → ∞. We also obtain the condition for the existence of
more » ... r the existence of a touchdown time T
doi:10.4134/bkms.2012.49.4.705 fatcat:xtibv45bo5bbhphepni5cylxme