Estimates for the quenching time of a parabolic equation modeling electrostatic MEMS

Details Estimates for the quenching time of a parabolic equation modeling electrostatic MEMS Estimates for the quenching time of a parabolic equation modeling electrostatic MEMS

2007-12-18

arxiv.org/abs/0712.3071v1

Mathematics

Analysis of PDEs

17 pages, 5 figures. Updated version -- if any -- of this paper can be downloaded from the website: http://www.birs.ca/~nassif

Scientific paper

The singular parabolic problem $u_t=\Delta u -\frac{\lambda f(x)}{(1+u)^2}$ on a bounded domain $\Omega$ 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 $\lambda$. As a byproduct, we prove that for sufficiently large $\lambda$, finite-time quenching must occur near the maximum point of the varying dielectric permittivity profile $f(x)$.

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