Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4182
DC FieldValueLanguage
dc.contributor.authorSeifert, Christian-
dc.contributor.authorTrostorff, Sascha-
dc.contributor.authorWaurick, Marcus-
dc.date.accessioned2022-02-28T07:45:07Z-
dc.date.available2022-02-28T07:45:07Z-
dc.date.issued2021-09-28-
dc.identifier.citationOperator Theory: Advances and Applications 287: 259-273 (2022-01-01)de_DE
dc.identifier.isbn978-3-030-89397-2de_DE
dc.identifier.isbn978-3-030-89396-5de_DE
dc.identifier.urihttp://hdl.handle.net/11420/11756-
dc.description.abstractPreviously, we focussed on evolutionary equations of the form (∂t,νM(∂t,ν)+A¯)U=F. $$\displaystyle \left (\overline {\partial _{t,\nu }M(\partial _{t,\nu })+A}\right )U=F.$$ In this chapter, where we turn back to well-posedness issues, we replace the material law operator M(∂t,ν), which is invariant under translations in time, by an operator of the form ℳ+∂t,ν−1N, $$\displaystyle \mathcal {M}+\partial _{t,\nu }^{-1}\mathcal {N},$$ where both ℳ and N are bounded linear operators in L2,ν(ℝ; H). Thus, it is the aim in the following to provide criteria on ℳ and N under which the operator ∂t,νℳ+N+A $$\displaystyle \partial _{t,\nu }\mathcal {M}+\mathcal {N}+A$$ is closable with continuous invertible closure in L2,ν(ℝ; H). In passing, we shall also replace the skew-selfadjointness of A by a suitable real part condition. Under additional conditions on ℳ and N, we will also see that the solution operator is causal. Finally, we will put the autonomous version of Picard’s theorem into perspective of the non-autonomous variant developed here.en
dc.language.isoende_DE
dc.publisherSpringerde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleNon-autonomous evolutionary equationsde_DE
dc.typeinBookde_DE
dc.identifier.doi10.15480/882.4182-
dc.type.dinibookPart-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-882.0173124-
tuhh.oai.showtruede_DE
tuhh.abstract.englishPreviously, we focussed on evolutionary equations of the form (∂t,νM(∂t,ν)+A¯)U=F. $$\displaystyle \left (\overline {\partial _{t,\nu }M(\partial _{t,\nu })+A}\right )U=F.$$ In this chapter, where we turn back to well-posedness issues, we replace the material law operator M(∂t,ν), which is invariant under translations in time, by an operator of the form ℳ+∂t,ν−1N, $$\displaystyle \mathcal {M}+\partial _{t,\nu }^{-1}\mathcal {N},$$ where both ℳ and N are bounded linear operators in L2,ν(ℝ; H). Thus, it is the aim in the following to provide criteria on ℳ and N under which the operator ∂t,νℳ+N+A $$\displaystyle \partial _{t,\nu }\mathcal {M}+\mathcal {N}+A$$ is closable with continuous invertible closure in L2,ν(ℝ; H). In passing, we shall also replace the skew-selfadjointness of A by a suitable real part condition. Under additional conditions on ℳ and N, we will also see that the solution operator is causal. Finally, we will put the autonomous version of Picard’s theorem into perspective of the non-autonomous variant developed here.de_DE
tuhh.publisher.doi10.1007/978-3-030-89397-2_16-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.4182-
tuhh.type.opusInBuch (Kapitel / Teil einer Monographie)-
dc.type.driverbookPart-
dc.type.casraiBook Chapter-
tuhh.container.startpage259de_DE
tuhh.container.endpage273de_DE
tuhh.relation.ispartofseriesOperator theoryde_DE
tuhh.relation.ispartofseriesnumber287de_DE
dc.identifier.scopus2-s2.0-85124410706de_DE
local.status.inpressfalsede_DE
local.type.versionpublishedVersionde_DE
datacite.resourceTypeBook Chapter-
datacite.resourceTypeGeneralText-
item.languageiso639-1en-
item.grantfulltextopen-
item.creatorOrcidSeifert, Christian-
item.creatorOrcidTrostorff, Sascha-
item.creatorOrcidWaurick, Marcus-
item.mappedtypeinBook-
item.tuhhseriesidOperator theory-
item.creatorGNDSeifert, Christian-
item.creatorGNDTrostorff, Sascha-
item.creatorGNDWaurick, Marcus-
item.seriesrefOperator theory;287-
item.fulltextWith Fulltext-
item.openairetypeinBook-
item.openairecristypehttp://purl.org/coar/resource_type/c_3248-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0001-9182-8687-
crisitem.author.orcid0000-0003-4498-3574-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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