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

2007/12/18 by Nassif Ghoussoub, Ghoussoub, Nassif, Yujin Guo +1 · 2 citations
Computer Science · Engineering · Mathematics · #35J50 #Advanced MEMS and NEMS Technologies #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #math.AP #msc:35J50

paper · pdf · doi:10.48550/arxiv.0712.3071

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

arxiv created 2007/12/18 · openalex publication_date 2007/12/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The singular parabolic problem u_t=Δu -(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).

Cited by

• On the quenching behavior of the MEMS with fringing field
• On semi-linear elliptic equation arising from Micro-Electromechanical Systems with contacting elastic membrane

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