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dc.contributor.authorValein J.
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.issn0363-0129
dc.identifier.urihttp://hdl.handle.net/20.500.11824/511
dc.description.abstractIn this paper we study the stabilization of the wa ve equation on general 1-d networks. For that, we transfer known observability results in the context of control problems of conservative systems (see [R. Dáger and E. Zuazua, Wave Propagation, Observation, and Control in 1-d Flexible Multi-structures, Math. Appl. 50, Springer-Verlag, Berlin, 2006]) into a weighted observability estimate for dissipative systems. Then we use an interpolation inequality similar to the one proved in [P. Bégout and F. Soria, J. Differential Equations, 240 (2007), pp. 324-356] to obtain the explicit decay estimates of the energy for smooth initial data. The obtained decay rate depends on the geometric and topological properties of the network. We also give some examples of particular networks in which our results apply, yielding different decay rates. © 2009 Society for Industrial and Applied Mathematics.
dc.formatapplication/pdf
dc.languageeng
dc.publisherSIAM Journal on Control and Optimization
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subjectNetwork
dc.subjectStabilization
dc.subjectWave equation
dc.titleStabilization of the wave equation on 1-D networks
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.identifier.doi10.1137/080733590
dc.relation.publisherversionhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-77955021500&doi=10.1137%2f080733590&partnerID=40&md5=787d047e77220e3a0d564c2a4049afab


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