On evolutionary [Gamma]-convergence for gradient systems : in memory of Eduard, Waldemar, and Elli Mielke

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume1915
dc.contributor.authorMielke, Alexander
dc.date.accessioned2016-03-24T17:37:22Z
dc.date.available2019-06-28T08:16:25Z
dc.date.issued2014
dc.description.abstractIn these notes we discuss general approaches for rigorously deriving limits of generalized gradient flows. Our point of view is that a generalized gradient system is defined in terms of two functionals, namely the energy functional E and the dissipation potential R or the associated dissipation distance. We assume that the functionals depend on a small parameter and that the associated gradient systems have solutions u. We investigate the question under which conditions the limits u of (subsequences of) the solutions u are solutions of the gradient system generated by the [Gamma]-limits E0 and R0. Here the choice of the right topology will be crucial awell as additional structural conditions. We cover classical gradient systems, where R is quadratic, and rate-independent systems as well as the passage from classical gradient to rate-independent systems. Various examples, such as periodic homogenization, are used to illustrate the abstract concepts and results.eng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn2198-5855
dc.identifier.urihttps://doi.org/10.34657/2799
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/3073
dc.language.isoengeng
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastikeng
dc.relation.issn0946-8633eng
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.eng
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.ger
dc.subject.ddc510eng
dc.subject.otherVariational evolutioneng
dc.subject.otherenergy functionaleng
dc.subject.otherdissipation potentialeng
dc.subject.otherdissipation distanceeng
dc.subject.othergradient flowseng
dc.subject.otherGamma convergenceeng
dc.subject.otherwell-prepared initial conditionseng
dc.subject.otherrate-independent systemseng
dc.subject.otherabstract chain-ruleeng
dc.subject.otherenerty-dissipation balance integrated evolutionary variational estimateeng
dc.subject.otherenergetic solutionseng
dc.titleOn evolutionary [Gamma]-convergence for gradient systems : in memory of Eduard, Waldemar, and Elli Mielkeeng
dc.typeReporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
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