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dc.contributor.authorPrivat Y.
dc.contributor.authorTrélat E.
dc.contributor.authorZuazua E.
dc.date.accessioned2017-02-21T08:18:18Z
dc.date.available2017-02-21T08:18:18Z
dc.date.issued2013-12-31
dc.identifier.issn1069-5869
dc.identifier.urihttp://hdl.handle.net/20.500.11824/517
dc.description.abstractIn this paper, we consider the homogeneous one-dimensional wave equation on [0,π] with Dirichlet boundary conditions, and observe its solutions on a subset ω of [0,π]. Let L∈(0,1). We investigate the problem of maximizing the observability constant, or its asymptotic average in time, over all possible subsets ω of [0,π] of Lebesgue measure Lπ. We solve this problem by means of Fourier series considerations, give the precise optimal value and prove that there does not exist any optimal set except for L=1/2. When L≠1/2 we prove the existence of solutions of a relaxed minimization problem, proving a no gap result. Following Hébrard and Henrot (Syst. Control Lett., 48:199-209, 2003; SIAM J. Control Optim., 44:349-366, 2005), we then provide and solve a modal approximation of this problem, show the oscillatory character of the optimal sets, the so called spillover phenomenon, which explains the lack of existence of classical solutions for the original problem.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.publisherJournal of Fourier Analysis and Applications
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectHarmonic analysis
dc.subjectObservability
dc.subjectOptimal design
dc.subjectWave equation
dc.titleOptimal Observation of the One-dimensional Wave Equation
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1007/s00041-013-9267-4
dc.relation.publisherversionhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84877070259&doi=10.1007%2fs00041-013-9267-4&partnerID=40&md5=072d845e5493ec8c0cb1706f44082207
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US


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