No Touchdown at Zero Points of the Permittivity Profile for the MEMS Problem

DOI10.1137/140970070zbMath1332.35160arXiv1405.6794OpenAlexW2017106433MaRDI QIDQ5264961

Philippe Souplet, Jong-Shenq Guo

Publication date: 21 July 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.6794

zbMATH Keywords

compactnessnonlinear parabolic problemtouchdownmicro-electro-mechanical systemspermittivity profilequenching pointstype I estimate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Electromagnetic effects in solid mechanics (74F15) Membranes (74K15) Blow-up in context of PDEs (35B44)

Related Items (15)

On qualitative properties of solutions to microelectromechanical systems with general permittivity ⋮ Self-similar solutions for a quenching problem with spatially dependent nonlinearity ⋮ On some touchdown behaviors of the generalized MEMS device equation ⋮ Excluding blowup at zero points of the potential by means of Liouville-type theorems ⋮ Touchdown solutions in general MEMS models ⋮ A free boundary value problem modelling microelectromechanical systems with general permittivity ⋮ Unnamed Item ⋮ A note on model reduction for microelectromechanical systems ⋮ Some singular equations modeling MEMS ⋮ Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt system ⋮ A survey on second order free boundary value problems modelling MEMS with general permittivity profile ⋮ Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity ⋮ Singular behavior of an electrostatic-elastic membrane system with an external pressure ⋮ Profile of a touch-down solution to a nonlocal MEMS model ⋮ Radial single point rupture solutions for a general MEMS model

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