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dc.contributor.authorZhang X.
dc.contributor.authorZheng C.
dc.contributor.authorZuazua E.
dc.date.accessioned2017-02-21T08:18:17Z
dc.date.available2017-02-21T08:18:17Z
dc.date.issued2009-12-31
dc.identifier.issn1078-0947
dc.identifier.urihttp://hdl.handle.net/20.500.11824/513
dc.description.abstractIn this paper we study the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. We prove that the projection of the solution in an appropriate filtered space is exactly controllable with uniformly bounded cost with respect to the time-step. In this way, the well-known exact-controllability property of the wave equation can be reproduced as the limit, as the time step h → 0, of the controllability of projections of the time-discrete one. By duality these results are equivalent to deriving uniform observability estimates (with respect to h → 0) within a class of solutions of the time-discrete problem in which the high frequency components have been filtered. The later is established by means of a time-discrete version of the classical multiplier technique. The optimality of the order of the filtering parameter is also established, although a careful analysis of the expected velocity of propagation of time-discrete waves indicates that its actual value could be improved.
dc.formatapplication/pdf
dc.languageeng
dc.publisherDiscrete and Continuous Dynamical Systems
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subjectExact controllability
dc.subjectFiltering
dc.subjectMultiplier technique
dc.subjectObservability
dc.subjectTime discretization
dc.subjectWave equation
dc.titleTime discrete wave equations: Boundary observability and control
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.identifier.doi10.3934/dcds.2009.23.571
dc.relation.publisherversionhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-57849119795&doi=10.3934%2fdcds.2009.23.571&partnerID=40&md5=de9f85819470bd8c9f3d5d2faed56c3d


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