Estimates for the Quenching Time of a Parabolic Equation Modeling Electrostatic MEMS
Nassif Ghoussoub, Yujin Guo · Methods and Applications of Analysis · 2008
The singular parabolic problem ut = ∆u -λf (x) (1+u) 2 on a bounded domain Ω of R N with Dirichlet boundary conditions, models the dynamic deflection of an elastic membrane in a simple electrostatic Micro-Electromechanical System (MEMS) device.In this paper, we analyze and estimate the quenching time of the elastic membrane in terms of the applied voltage -represented here by λ.As a byproduct, we prove that for sufficiently large λ, finite-time quenching must occur near the maximum point of the varying dielectric permittivity profile f (x).