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SHARP REACHABILITY RESULTS FOR THE HEAT EQUATION IN ONE SPACE DIMENSION

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorKELLAY, Karim
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorNORMAND, Thomas
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTUCSNAK, Marius
dc.date.accessioned2024-04-04T02:59:49Z
dc.date.available2024-04-04T02:59:49Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192771
dc.description.abstractEnThis paper gives a complete characterization of the reachable space for a system described by the 1D heat equation with L2 (with respect to time) Dirichlet boundary controls at both ends. More precisely, we prove that this space coincides with the sum of two spaces of analytic functions (of Bergman type). These results are then applied to give a complete description of the reachable space via inputs which are n-times differentiable functions of time. Moreover, we establish a connection between the norm in the obtained sum of Bergman spaces and the cost of null controllability in small time. Finally we show that our methods yield new complex analytic results on the sums of Bergman spaces in infinite sectors.
dc.language.isoen
dc.title.enSHARP REACHABILITY RESULTS FOR THE HEAT EQUATION IN ONE SPACE DIMENSION
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 classique [math.CA]
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-02302165
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02302165v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=KELLAY,%20Karim&NORMAND,%20Thomas&TUCSNAK,%20Marius&rft.genre=preprint


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