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

2016/02/25 by Nikos Kavallaris, Andrew Lacey, Kavallaris, Nikos +3 · 1 citation
Mathematics · #35J60 #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J60 #msc:35K55

paper · pdf · doi:10.48550/arxiv.1602.07888

19 pages, 6 figures

arxiv created 2016/02/25 · arxiv updated 2016/02/26

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.

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