Optimal velocity control of a viscous Cahn-Hilliard system with convection and dynamic boundary conditions

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume2427
dc.contributor.authorColli, Pierluigi
dc.contributor.authorGilardi, Gianni
dc.contributor.authorSprekels, Jürgen
dc.date.accessioned2017-11-11T06:32:13Z
dc.date.available2019-06-28T08:04:12Z
dc.date.issued2017
dc.description.abstractIn this paper, we investigate a distributed optimal control problem for a convective viscous CahnHilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents an additional difficulty for the analysis. The nonlinearities in the bulk and surface free energies are of logarithmic type, which entails that the thermodynamic forces driving the phase separation process may become singular. We show existence for the optimal control problem under investigation, prove the Fréchet differentiability of the associated control-to-state mapping in suitable Banach spaces, and derive the first-order necessary optimality conditions in terms of a variational inequality and the associated adjoint system. Due to the strong nonlinear couplings between state variables and control, the corresponding proofs require a considerable analytical effort.eng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn2198-5855
dc.identifier.urihttps://doi.org/10.34657/2938
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/2160
dc.language.isoengeng
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastikeng
dc.relation.doihttps://doi.org/10.20347/WIAS.PREPRINT.2427
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.otherCahn–Hilliard systemeng
dc.subject.otherconvection termeng
dc.subject.otherdynamic boundary conditionseng
dc.subject.otheroptimal velocity controleng
dc.subject.otheroptimality conditionseng
dc.subject.otheradjoint state systemeng
dc.titleOptimal velocity control of a viscous Cahn-Hilliard system with convection and dynamic boundary conditionseng
dc.typeReporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
1003537006.pdf
Size:
306.09 KB
Format:
Adobe Portable Document Format
Description: