DC FieldValueLanguage
dc.contributor.authorGallaun, Dennis-
dc.contributor.authorSeifert, Christian-
dc.contributor.authorTautenhahn, Martin-
dc.date.accessioned2021-11-09T11:00:09Z-
dc.date.available2021-11-09T11:00:09Z-
dc.date.issued2020-
dc.identifier.citationSIAM Journal on Control and Optimization 58 (4): 2639-2657 (2020)de_DE
dc.identifier.issn1095-7138de_DE
dc.identifier.urihttp://hdl.handle.net/11420/10845-
dc.description.abstractLet X, Y be Banach spaces, (St)t≥ 0 a C0-semigroup on X, A the corresponding infinitesimal generator on X, C a bounded linear operator from X to Y , and T 0. We consider the system x(̇t) = Ax(t), y(t) = Cx(t), t ∈ (0, T], x(0) = x0 ∈ X. We provide sufficient conditions such that this system satisfies a final state observability estimate in Lr((0, T); Y ), r ∈ [1,∞ ]. These sufficient conditions are given by an uncertainty relation and a dissipation estimate. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider the example where A is an elliptic operator in Lp(Rd) for 1 p ∞ and where C = 1E is the restriction onto a thick set E ⊂ Rd. In this case, we show that the above system satisfies a final state observability estimate if and only if E ⊂ Rd is a thick set. Finally, we make use of the well-known relation between observability and null-controllability of the predual system and investigate bounds on the corresponding control costs.en
dc.language.isoende_DE
dc.relation.ispartofSIAM journal on control and optimizationde_DE
dc.subjectBanach spacede_DE
dc.subjectC0-semigroupsde_DE
dc.subjectControl costsde_DE
dc.subjectElliptic operatorsde_DE
dc.subjectNull-controllabilityde_DE
dc.subjectObservability estimatede_DE
dc.titleSufficient criteria and sharp geometric conditions for observability in banach spacesde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishLet X, Y be Banach spaces, (St)t≥ 0 a C0-semigroup on X, A the corresponding infinitesimal generator on X, C a bounded linear operator from X to Y , and T 0. We consider the system x(̇t) = Ax(t), y(t) = Cx(t), t ∈ (0, T], x(0) = x0 ∈ X. We provide sufficient conditions such that this system satisfies a final state observability estimate in Lr((0, T); Y ), r ∈ [1,∞ ]. These sufficient conditions are given by an uncertainty relation and a dissipation estimate. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider the example where A is an elliptic operator in Lp(Rd) for 1 p ∞ and where C = 1E is the restriction onto a thick set E ⊂ Rd. In this case, we show that the above system satisfies a final state observability estimate if and only if E ⊂ Rd is a thick set. Finally, we make use of the well-known relation between observability and null-controllability of the predual system and investigate bounds on the corresponding control costs.de_DE
tuhh.publisher.doi10.1137/19m1266769-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue4de_DE
tuhh.container.volume58de_DE
tuhh.container.startpage2639de_DE
tuhh.container.endpage2657de_DE
dc.identifier.scopus2-s2.0-85091312780-
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.languageiso639-1en-
item.grantfulltextnone-
item.creatorOrcidGallaun, Dennis-
item.creatorOrcidSeifert, Christian-
item.creatorOrcidTautenhahn, Martin-
item.mappedtypeArticle-
item.creatorGNDGallaun, Dennis-
item.creatorGNDSeifert, Christian-
item.creatorGNDTautenhahn, Martin-
item.fulltextNo Fulltext-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0001-9182-8687-
crisitem.author.orcid0000-0002-6169-0493-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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