On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control. (June 2016)

• Record Type: Journal Article
• Authors: Kavallaris, Nikos I.; Lacey, Andrew A.; Nikolopoulos, Christos V.
• Is Part Of: Nonlinear analysis. Volume 138(2016)
• Page Start: 189
• Page End: 206
• Publication Date: 2016-06
• Subjects: primary 35K55 35J60 -- secondary 74H35 74G55 74K15; Electrostatic MEMS -- Touchdown -- Quenching; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.02.001
• Languages: English
• ISSNs: 0362-546X

Abstract

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.