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

dc.creatorGhoussoub, Nassif
dc.creatorGuo, Yujin
dc.date2007-12-18
dc.date.accessioned2026-07-07T08:50:16Z
dc.date.available2026-07-07T08:50:16Z
dc.descriptionThe 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 $f(x)$.
dc.description17 pages, 5 figures. Updated version -- if any -- of this paper can be downloaded from the website: http://www.birs.ca/~nassif
dc.identifierhttps://arxiv.org/abs/0712.3071
dc.identifierhttp://arxiv.org/abs/0712.3071
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144546
dc.subjectAnalysis of PDEs
dc.subject35J50
dc.titleEstimates for the quenching time of a parabolic equation modeling electrostatic MEMS
dc.typetext

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