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Insensitizing controls for the heat equation with respect to boundary variations

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorERVEDOZA, Sylvain
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLISSY, Pierre
hal.structure.identifierTOkamaks and NUmerical Simulations [TONUS]
hal.structure.identifierInstitut de Recherche Mathématique Avancée [IRMA]
hal.structure.identifierInstitut universitaire de France [IUF]
dc.contributor.authorPRIVAT, Yannick
dc.date.accessioned2024-04-04T02:39:44Z
dc.date.available2024-04-04T02:39:44Z
dc.date.created2020-12-18
dc.date.issued2022
dc.identifier.issn2429-7100
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191000
dc.description.abstractEnThis article is dedicated to insensitization issues of a quadratic functional involving the solution of the linear heat equation with respect to domains variations. This work can be seen as a continuation of [P. Lissy, Y. Privat, and Y. Simpor\'e. Insensitizing control for linear and semi-linear heat equations with partially unknown domain. ESAIM Control Optim. Calc. Var., 25:Art. 50, 21, 2019], insofar as we generalize several of the results it contains and investigate new related properties. In our framework, we consider boundary variations of the spatial domain on which the solution of the PDE is defined at each time, and investigate three main issues: (i) approximate insensitization, (ii) approximate insensitization combined with an exact insensitization for a finite-dimensional subspace, and (iii) exact insensitization. We provide positive answers to questions (i) and (ii) and partial results to question (iii).
dc.language.isoen
dc.publisherÉcole polytechnique
dc.subject.enheat equation
dc.subject.enexact/approximate control
dc.subject.endomain variations
dc.subject.eninsensitization properties
dc.subject.enBrouwer fixed-point theorem
dc.title.enInsensitizing controls for the heat equation with respect to boundary variations
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
dc.identifier.arxiv2012.14327
bordeaux.journalJournal de l'École polytechnique — Mathématiques
bordeaux.page1397--1429
bordeaux.volumeTome 9
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03083177
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03083177v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20de%20l'%C3%89cole%20polytechnique%20%E2%80%94%20Math%C3%A9matiques&rft.date=2022&rft.volume=Tome%209&rft.spage=1397--1429&rft.epage=1397--1429&rft.eissn=2429-7100&rft.issn=2429-7100&rft.au=ERVEDOZA,%20Sylvain&LISSY,%20Pierre&PRIVAT,%20Yannick&rft.genre=article


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