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A unified strategy for observability of waves in an annulus with various boundary conditions

hal.structure.identifierÉquipe Méthodes et Algorithmes en Commande [LAAS-MAC]
dc.contributor.authorBAUDOUIN, Lucie
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorDARDÉ, Jérémi
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorERVEDOZA, Sylvain
hal.structure.identifierUniversidad Tecnica Federico Santa Maria [Valparaiso] [UTFSM]
dc.contributor.authorMERCADO, Alberto
dc.date.accessioned2024-04-04T02:42:40Z
dc.date.available2024-04-04T02:42:40Z
dc.date.created2022-01-22
dc.date.issued2022-01
dc.identifier.issn1582-3067
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191263
dc.description.abstractEnIn this work, we develop a unified strategy which allows to derive observability results for waves in an annulus when the observation is done on the external boundary and under various boundary conditions at the internal boundary. Our approach is based on the fact that the observability of a linear abstract conservative system is equivalent to a suitable resolvent estimate. We develop a full machinery to derive suitable resolvent estimates under some weak assumptions on the boundary condition on the internal sphere, which are shown to be close to sharp. In fact, our strategy allows to exclude the existence of trapped rays close to the internal sphere when the boundary conditions satisfy a suitable assumption. As an application, we apply our results to several wave models.
dc.description.sponsorshipNouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux - ANR-20-CE40-0009
dc.description.sponsorshipCentre International de Mathématiques et d'Informatique (de Toulouse) - ANR-11-LABX-0040
dc.language.isoen
dc.publisherRomanian Academy of Sciences
dc.title.enA unified strategy for observability of waves in an annulus with various boundary conditions
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalMathematical Reports
bordeaux.page59-112
bordeaux.volume24
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1-2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03401646
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03401646v1
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