Optimal boundary control of a viscous Cahn-Hilliard system with dynamic boundary condition and double obstacle potentials

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume2006
dc.contributor.authorColli, Pierluigi
dc.contributor.authorFarshbaf Shaker, Mohammad Hassan
dc.contributor.authorGilardi, Gianni
dc.contributor.authorSprekels, Jürgen
dc.date.accessioned2016-03-24T17:37:01Z
dc.date.available2019-06-28T08:12:36Z
dc.date.issued2014
dc.description.abstractIn this paper, we investigate optimal boundary control problems for Cahn--Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace--Beltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, Farshbaf-Shaker, Sprekels (see Appl. Math. Optim., 2014) to the (simpler) Allen--Cahn case, is the following: we use the results that were recently established by Colli, Gilardi, Sprekels in the preprint arXiv:1407.3916 [math.AP] for the case of (differentiable) logarithmic potentials and perform a so-called ``deep quench limit''. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.eng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn2198-5855
dc.identifier.urihttps://doi.org/10.34657/2900
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/2879
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.otherOptimal controleng
dc.subject.otherparabolic obstacle problemseng
dc.subject.otherMPECseng
dc.subject.otherdynamic boundary conditionseng
dc.subject.otheroptimality conditionseng
dc.titleOptimal boundary control of a viscous Cahn-Hilliard system with dynamic boundary condition and double obstacle potentialseng
dc.typeReporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
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