Weighted energy-dissipation functionals for gradient flows

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume1400
dc.contributor.authorMielke, Alexander
dc.contributor.authorStefanelli, Ulisse
dc.date.accessioned2016-03-24T17:38:26Z
dc.date.available2019-06-28T08:03:42Z
dc.date.issued2009
dc.description.abstractWe investigate a global-in-time variational approach to abstract evolution by means of the weighted energy-dissipation functionals proposed by Mielke & Ortiz in ``A class of minimum principles for characterizing the trajectories of dissipative systems''. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization. Applications of the theory to various classes of parabolic PDE problems are presented. In particular, we focus on two examples of microstructure evolution from S. Conti and M. Ortiz ``Minimum principles for the trajectories of systems governed by rate problems'eng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn0946-8633
dc.identifier.urihttps://doi.org/10.34657/3481
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/2083
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.subjectVariational principleeng
dc.subjectgradient floweng
dc.subjectconvergenceeng
dc.subject.ddc510eng
dc.titleWeighted energy-dissipation functionals for gradient flowseng
dc.typereporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
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