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dc.contributor.authorPrivat Y.
dc.contributor.authorTrélat E.
dc.contributor.authorZuazua E.
dc.dateinfo:eu-repo/date/embargoEnd/2016-12-31
dc.date.accessioned2016-06-13T13:33:50Z
dc.date.available2016-06-13T13:33:50Z
dc.date.issued2015-12-31
dc.identifier.issn1078-0947
dc.identifier.urihttp://hdl.handle.net/20.500.11824/250
dc.description.abstractWe consider the homogeneous wave equation on a bounded open connected subset Ω of IRn. Some initial data being specified, we consider the problem of determining a measurable subset ω of Ω maximizing the L2-norm of the restriction of the corresponding solution to ω over a time interval [0, T], over all possible subsets of Ω having a certain prescribed measure. We prove that this problem always has at least one solution and that, if the initial data satisfy some analyticity assumptions, then the optimal set is unique and moreover has a finite number of connected components. In contrast, we construct smooth but not analytic initial conditions for which the optimal set is of Cantor type and in particular has an infinite number of connected components.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.publisherDiscrete and Continuous Dynamical Systems- Series A
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectCalculus of variations.
dc.subjectCantor set
dc.subjectFourier series
dc.subjectOptimal domain
dc.subjectWave equation
dc.titleComplexity and regularity of maximal energy domains for the wave equation with fixed initial data
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.3934/dcds.2015.35.6133
dc.relation.publisherversionhttps://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11217
dc.relation.projectIDES/6PN/MTM2011-29306-C02-01en_US
dc.relation.projectIDES/1PE/SEV-2013-0323en_US
dc.rights.accessRightsinfo:eu-repo/semantics/embargoedAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US


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