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Reachability results for perturbed heat equations

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorERVEDOZA, Sylvain
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierControl And GEometry [CaGE]
dc.contributor.authorLE BALC'H, Kévin
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTUCSNAK, Marius
dc.date.accessioned2024-04-04T02:39:30Z
dc.date.available2024-04-04T02:39:30Z
dc.date.issued2022-11-15
dc.identifier.issn0022-1236
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190974
dc.description.abstractEnThis work studies the reachable space of infinite dimensional control systems which are null controllable in any positive time, the typical example being the heat equation controlled from the boundary or from an arbitrary open set. The focus is on the robustness of the reachable space with respect to linear or nonlinear perturbations of the generator. More precisely, our first main results asserts that this space is invariant under perturbations which are small (in an appropriate sense). A second main result asserts the invariance of the reachable space with respect to perturbations which are compact (again in an appropriate sense), provided that a Hautus type condition is satisfied. Moreover, our methods give precise information on the behavior of the reachable space when the generator is perturbed by a class of nonlinear operators. When applied to the classical heat equation, our results provide detailed information on the reachable space when the generator is perturbed by a small potential or by a class of non local operators, and in particular in one space dimension, we deduce from our analysis that the reachable space for perturbations of the 1-d heat equation is a space of holomorphic functions. We also show how our approach leads to reachability results for a class of semi-linear parabolic equations.
dc.description.sponsorshipNouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux - ANR-20-CE40-0009
dc.description.sponsorshipInitiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
dc.language.isoen
dc.publisherElsevier
dc.title.enReachability results for perturbed heat equations
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalJournal of Functional Analysis
bordeaux.volume283
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue10
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03380745
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03380745v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Functional%20Analysis&rft.date=2022-11-15&rft.volume=283&rft.issue=10&rft.eissn=0022-1236&rft.issn=0022-1236&rft.au=ERVEDOZA,%20Sylvain&LE%20BALC'H,%20K%C3%A9vin&TUCSNAK,%20Marius&rft.genre=article


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