Optimal control of an Allen-Cahn equation with singular potentials and dynamic boundary condition

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume1750
dc.contributor.authorColli, Pierluigi
dc.contributor.authorSprekels, Jürgen
dc.date.accessioned2016-03-24T17:37:27Z
dc.date.available2019-06-28T08:22:54Z
dc.date.issued2012
dc.description.abstractIn this paper, we investigate optimal control problems for AllenCahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. Parabolic problems with nonlinear dynamic boundary conditions involving the LaplaceBeltrami operation have recently drawn increasing attention due to their importance in applications, while their optimal control was apparently never studied before. In this paper, we first extend known well-posedness and regularity results for the state equation and then show the existence of optimal controls and that the control-to-state mapping is twice continuously Fréchet differentiable between appropriate function spaces. Based on these results, we establish the firstorder necessary optimality conditions in terms of a variational inequality and the adjoint state equation, and we prove second-order sufficient optimality conditionseng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn0946-8633
dc.identifier.urihttps://doi.org/10.34657/2931
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/3342
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 problemseng
dc.subject.otherdynamic boundary conditionseng
dc.subject.otheroptimality conditionseng
dc.titleOptimal control of an Allen-Cahn equation with singular potentials and dynamic boundary conditioneng
dc.typeReporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
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