Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4179
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dc.contributor.authorSeifert, Christian-
dc.contributor.authorTrostorff, Sascha-
dc.contributor.authorWaurick, Marcus-
dc.date.accessioned2022-02-24T08:37:54Z-
dc.date.available2022-02-24T08:37:54Z-
dc.date.issued2021-09-28-
dc.identifier.citationOperator Theory: Advances and Applications 287: 167-188 (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/11420/11753-
dc.description.abstractIn this chapter we study the exponential stability of evolutionary equations. Roughly speaking, exponential stability of a well-posed evolutionary equation (∂t,νM(∂t,ν)+A)U=F (∂ t,ν M(∂ t,ν )+A)U=F means that exponentially decaying right-hand sides F lead to exponentially decaying solutions U. The main problem in defining the notion of exponential decay for a solution of an evolutionary equation is the lack of continuity with respect to time, so a pointwise definition would not make sense in this framework. Instead, we will use our exponentially weighted spaces L2,ν(ℝ; H), but this time for negative ν, and define the exponential stability by the invariance of these spaces under the solution operator associated with the evolutionary equation under consideration.en
dc.language.isoende_DE
dc.publisherSpringerde_DE
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/de_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleExponential stability of evolutionary equationsde_DE
dc.typeinBookde_DE
dc.identifier.doi10.15480/882.4179-
dc.type.dinibookPart-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-882.0173091-
tuhh.oai.showtruede_DE
tuhh.abstract.englishIn this chapter we study the exponential stability of evolutionary equations. Roughly speaking, exponential stability of a well-posed evolutionary equation (∂t,νM(∂t,ν)+A)U=F (∂ t,ν M(∂ t,ν )+A)U=F means that exponentially decaying right-hand sides F lead to exponentially decaying solutions U. The main problem in defining the notion of exponential decay for a solution of an evolutionary equation is the lack of continuity with respect to time, so a pointwise definition would not make sense in this framework. Instead, we will use our exponentially weighted spaces L2,ν(ℝ; H), but this time for negative ν, and define the exponential stability by the invariance of these spaces under the solution operator associated with the evolutionary equation under consideration.de_DE
tuhh.publisher.doi10.1007/978-3-030-89397-2_11-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.4179-
tuhh.type.opusInBuch (Kapitel / Teil einer Monographie)-
dc.type.driverbookPart-
dc.type.casraiBook Chapter-
tuhh.container.startpage167de_DE
tuhh.container.endpage188de_DE
dc.rights.nationallicensefalsede_DE
tuhh.relation.ispartofseriesOperator theoryde_DE
tuhh.relation.ispartofseriesnumber287de_DE
dc.identifier.scopus2-s2.0-85124388514de_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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