A hyperbolic non-local problem modelling MEMS technology

Kavallaris, NI; Lacey, AA; Nikolopoulos, CV; Tzanetis, DE

dc.contributor.author	Kavallaris, NI	en
dc.contributor.author	Lacey, AA	en
dc.contributor.author	Nikolopoulos, CV	en
dc.contributor.author	Tzanetis, DE	en
dc.date.accessioned	2014-03-01T01:34:53Z
dc.date.available	2014-03-01T01:34:53Z
dc.date.issued	2011	en
dc.identifier.issn	0035-7596	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20924
dc.subject	Electrostatic mems	en
dc.subject	Hyperbolic non-local problems	en
dc.subject	Quenching of solution	en
dc.subject.classification	Mathematics	en
dc.subject.other	ELECTROSTATIC MEMS	en
dc.subject.other	QUENCHING PROBLEM	en
dc.subject.other	EQUATIONS	en
dc.subject.other	TOUCHDOWN	en
dc.title	A hyperbolic non-local problem modelling MEMS technology	en
heal.type	journalArticle	en
heal.identifier.primary	10.1216/RMJ-2011-41-2-505	en
heal.identifier.secondary	http://dx.doi.org/10.1216/RMJ-2011-41-2-505	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	In this work we study a non-local hyperbolic equation of the form u(tt) = u(xx) + lambda/(1 - u)(2) (1 + alpha integral(1)(0) (1/(1 - u)) dx)(2), with homogeneous Dirichlet boundary conditions and appropriate initial conditions. The problem models an idealized electrostatically actuated MEMS (Micro-Electro-Mechanical System) device. Initially we present the derivation of the model. Then we prove local existence of solutions for lambda > 0 and global existence for 0 < lambda < lambda_* for some positive lambda_, with zero initial conditions; similar results are obtained for other initial data. For larger values of the parameter lambda, i.e., when lambda > lambda(+) for some constant lambda(+)* >= lambda_* and with zero initial conditions, it is proved that the solution of the problem quenches in finite time; again similar results are obtained for other initial data. Finally the problem is solved numerically with a finite difference scheme. Various simulations of the solution of the problem are presented, illustrating the relevant theoretical results.	en
heal.publisher	ROCKY MT MATH CONSORTIUM	en
heal.journalName	Rocky Mountain Journal of Mathematics	en
dc.identifier.doi	10.1216/RMJ-2011-41-2-505	en
dc.identifier.isi	ISI:000291250200010	en
dc.identifier.volume	41	en
dc.identifier.issue	2	en
dc.identifier.spage	505	en
dc.identifier.epage	534	en