Estimates for the quenching time of a parabolic equation modeling electrostatic MEMS
| dc.creator | Ghoussoub, Nassif | |
| dc.creator | Guo, Yujin | |
| dc.date | 2007-12-18 | |
| dc.date.accessioned | 2026-07-07T08:50:16Z | |
| dc.date.available | 2026-07-07T08:50:16Z | |
| dc.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 $f(x)$. | |
| dc.description | 17 pages, 5 figures. Updated version -- if any -- of this paper can be downloaded from the website: http://www.birs.ca/~nassif | |
| dc.identifier | https://arxiv.org/abs/0712.3071 | |
| dc.identifier | http://arxiv.org/abs/0712.3071 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144546 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J50 | |
| dc.title | Estimates for the quenching time of a parabolic equation modeling electrostatic MEMS | |
| dc.type | text |