Mostrar el registro sencillo del ítem

Cost of observability inequalities for elliptic equations in 2-d with potentials and applications to control theory

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorERVEDOZA, Sylvain
hal.structure.identifierControl And GEometry [CaGE ]
dc.contributor.authorLE BALC’H, Kévin
dc.date.accessioned2024-04-04T02:32:33Z
dc.date.available2024-04-04T02:32:33Z
dc.date.created2022-03
dc.date.issued2023-04-10
dc.identifier.issn0360-5302
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190396
dc.description.abstractEnThe goal of this article is to obtain observability estimates for non-homogeneous elliptic equations in the presence of a potential, posed on a smooth bounded domain Ω in 2-d and observed from a non-empty open subset ω ⊂ Ω. More precisely, for every real-valued bounded potential V, our main result shows that, when Ω has a finite number of holes, the observability constant of the elliptic operator −∆ + V, with domain H^2 ∩ H^1_0(Ω), is of the form C exp (C |V|^{1/2} \log^{1/2}(|V|)) where C is a positive constant depending only on Ω and ω. Our methodology of proof is crucially based on the one recently developed by Logunov, Malinnikova, Nadirashvili, and Nazarov, in the context of the Landis conjecture on exponential decay of solutions to homogeneous elliptic equations in the plane. The main difference and additional difficulty is that the zero set of the solutions to elliptic equations with source term can be very intricate and should be dealt with carefully. As a consequence of these new observability estimates, we obtain new results concerning control of semi-linear elliptic equations in the spirit of Fernández-Cara, Zuazua's open problem concerning small-time global null-controllability of slightly super-linear heat equations.
dc.description.sponsorshipNouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux - ANR-20-CE40-0009
dc.language.isoen
dc.publisherTaylor & Francis
dc.subject.enQuantitative unique continuation
dc.subject.enElliptic equations
dc.subject.enControl
dc.title.enCost of observability inequalities for elliptic equations in 2-d with potentials and applications to control theory
dc.typeArticle de revue
dc.identifier.doi10.1080/03605302.2023.2190526
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalCommunications in Partial Differential Equations
bordeaux.page623--677
bordeaux.volume48
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03616317
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03616317v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Partial%20Differential%20Equations&rft.date=2023-04-10&rft.volume=48&rft.issue=4&rft.spage=623--677&rft.epage=623--677&rft.eissn=0360-5302&rft.issn=0360-5302&rft.au=ERVEDOZA,%20Sylvain&LE%20BALC%E2%80%99H,%20K%C3%A9vin&rft.genre=article


Archivos en el ítem

ArchivosTamañoFormatoVer

No hay archivos asociados a este ítem.

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem