DC FieldValueLanguage
dc.contributor.authorBombach, Clemens-
dc.contributor.authorGabel, Fabian Nuraddin Alexander-
dc.contributor.authorSeifert, Christian-
dc.contributor.authorTautenhahn, Martin-
dc.date.accessioned2022-05-25T08:08:52Z-
dc.date.available2022-05-25T08:08:52Z-
dc.date.issued2022-03-16-
dc.identifier.citationarXiv: 2203.08469 (2022)de_DE
dc.identifier.urihttp://hdl.handle.net/11420/12715-
dc.description.abstractWe study non-autonomous observation systems align* ẋ(t) = A(t) x(t), y(t) = C(t) x(t), x(0) = x₀∈ X, align* where (A(t)) is a strongly measurable family of closed operators on a Banach space X and (C(t)) is a family of bounded observation operators from X to a Banach space Y. Based on an abstract uncertainty principle and a dissipation estimate, we prove that the observation system satisfies a final-state observability estimate in Lʳ(E; Y) for measurable subsets E ⊆ [0,T], T > 0. An application of the above result to families of uniformly strongly elliptic differential operators A(t) on Lᵖ(ℝᵈ) and observation operators C(t)u = 𝟏Ω₍t₎ u is presented. In this setting, we give sufficient and necessary geometric conditions on the family of sets (Ω(t)) such that the corresponding observation system satisfies a final-state observability estimate.en
dc.language.isoende_DE
dc.subjectFunctional Analysisde_DE
dc.subjectAnalysis of PDEsde_DE
dc.subjectOptimization and Controlde_DE
dc.subject35Q93, 47N70 (Primary) 93B07, 93B28 (Secondary)de_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleObservability for non-autonomous systemsde_DE
dc.typePreprintde_DE
dc.type.dinipreprint-
dcterms.DCMITypeText-
tuhh.abstract.englishWe study non-autonomous observation systems align* ẋ(t) = A(t) x(t), y(t) = C(t) x(t), x(0) = x₀∈ X, align* where (A(t)) is a strongly measurable family of closed operators on a Banach space X and (C(t)) is a family of bounded observation operators from X to a Banach space Y. Based on an abstract uncertainty principle and a dissipation estimate, we prove that the observation system satisfies a final-state observability estimate in Lʳ(E; Y) for measurable subsets E ⊆ [0,T], T > 0. An application of the above result to families of uniformly strongly elliptic differential operators A(t) on Lᵖ(ℝᵈ) and observation operators C(t)u = 𝟏Ω₍t₎ u is presented. In this setting, we give sufficient and necessary geometric conditions on the family of sets (Ω(t)) such that the corresponding observation system satisfies a final-state observability estimate.de_DE
tuhh.publisher.doi10.48550/arXiv.2203.08469-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opusPreprint (Vorabdruck)-
dc.type.driverpreprint-
dc.type.casraiOther-
dc.identifier.arxiv2203.08469de_DE
local.status.inpressfalsede_DE
datacite.resourceTypeOther-
datacite.resourceTypeGeneralText-
item.languageiso639-1en-
item.grantfulltextnone-
item.creatorOrcidBombach, Clemens-
item.creatorOrcidGabel, Fabian Nuraddin Alexander-
item.creatorOrcidSeifert, Christian-
item.creatorOrcidTautenhahn, Martin-
item.mappedtypePreprint-
item.creatorGNDBombach, Clemens-
item.creatorGNDGabel, Fabian Nuraddin Alexander-
item.creatorGNDSeifert, Christian-
item.creatorGNDTautenhahn, Martin-
item.fulltextNo Fulltext-
item.openairetypePreprint-
item.openairecristypehttp://purl.org/coar/resource_type/c_816b-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0002-8053-0284-
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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