A hyperbolic non-local problem modelling MEMS technology

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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 http://hdl.handle.net/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

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