On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control

Andrew Alfred Lacey; Nikos Kavallaris; Christos Nikolopoulos

doi:10.1016/j.na.2016.02.001

On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control

Andrew Alfred Lacey, Nikos Kavallaris, Christos Nikolopoulos

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Abstract

We consider a nonlocal parabolic model for a micro–electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a situation where there is no steady state. It is also shown that quenching occurs at a single point and a bound on the approach to touchdown is obtained. Numerical simulations illustrating the results are given.

Original language	English
Pages (from-to)	189–206
Number of pages	18
Journal	Nonlinear Analysis: Theory, Methods and Applications
Volume	138
Early online date	28 Feb 2016
DOIs	https://doi.org/10.1016/j.na.2016.02.001
Publication status	Published - Jun 2016

Keywords

Electrostatic MEMS
Touchdown
Quenching

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title = "On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control",

abstract = "We consider a nonlocal parabolic model for a micro–electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a situation where there is no steady state. It is also shown that quenching occurs at a single point and a bound on the approach to touchdown is obtained. Numerical simulations illustrating the results are given.",

keywords = "Electrostatic MEMS, Touchdown, Quenching",

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T1 - On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control

AU - Lacey, Andrew Alfred

AU - Kavallaris, Nikos

AU - Nikolopoulos, Christos

PY - 2016/6

Y1 - 2016/6

N2 - We consider a nonlocal parabolic model for a micro–electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a situation where there is no steady state. It is also shown that quenching occurs at a single point and a bound on the approach to touchdown is obtained. Numerical simulations illustrating the results are given.

AB - We consider a nonlocal parabolic model for a micro–electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a situation where there is no steady state. It is also shown that quenching occurs at a single point and a bound on the approach to touchdown is obtained. Numerical simulations illustrating the results are given.

KW - Electrostatic MEMS

KW - Touchdown

KW - Quenching

U2 - 10.1016/j.na.2016.02.001

DO - 10.1016/j.na.2016.02.001

M3 - Article

SN - 0362-546X

VL - 138

SP - 189

EP - 206

JO - Nonlinear Analysis: Theory, Methods and Applications

JF - Nonlinear Analysis: Theory, Methods and Applications

ER -

On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control

Abstract

Keywords

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