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Reachable states and holomorphic function spaces for the 1-D heat equation

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorORSONI, Marcu-Antone
dc.date.accessioned2024-04-04T03:00:02Z
dc.date.available2024-04-04T03:00:02Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192792
dc.description.abstractEnThe description of the reachable states of the heat equation is one of the central questions in control theory. The aim of this work is to present new results for the 1-D heat equation with boundary control on the segment [0, π]. In this situation it is known that the reachable states are holomorphic in a square D the diagonal of which is given by [0, π]. The most precise results obtained recently say that the reachable space is contained between two well known spaces of analytic function: the Smirnov space E^2(D) and the Bergman space A^2(D). We show that the reachable states are exactly the sum of two Bergman spaces on sectors the intersection of which is D. In order to get a more precise information on this sum of Bergman spaces, we also prove that it includes the Smirnov-Zygmund space E_{LlogL}(D) as well as a certain weighted Bergman space on D.
dc.language.isoen
dc.title.enReachable states and holomorphic function spaces for the 1-D heat equation
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.identifier.arxiv1909.01644
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-02275568
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02275568v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ORSONI,%20Marcu-Antone&rft.genre=preprint


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