Estimates for the quenching time of a parabolic equation modeling electrostatic MEMS
Abstract
Description
The singular parabolic problem $u_t=Δu -\frac{λf(x)}{(1+u)^2}$ 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 $f(x)$.
17 pages, 5 figures. Updated version -- if any -- of this paper can be downloaded from the website: http://www.birs.ca/~nassif
17 pages, 5 figures. Updated version -- if any -- of this paper can be downloaded from the website: http://www.birs.ca/~nassif