Optimal boundary control of a viscous Cahn-Hilliard system with dynamic boundary condition and double obstacle potentials
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2006 | |
dc.contributor.author | Colli, Pierluigi | |
dc.contributor.author | Farshbaf Shaker, Mohammad Hassan | |
dc.contributor.author | Gilardi, Gianni | |
dc.contributor.author | Sprekels, Jürgen | |
dc.date.accessioned | 2016-03-24T17:37:01Z | |
dc.date.available | 2019-06-28T08:12:36Z | |
dc.date.issued | 2014 | |
dc.description.abstract | In 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.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2900 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2879 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This 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.license | Dieses 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.ddc | 510 | eng |
dc.subject.other | Optimal control | eng |
dc.subject.other | parabolic obstacle problems | eng |
dc.subject.other | MPECs | eng |
dc.subject.other | dynamic boundary conditions | eng |
dc.subject.other | optimality conditions | eng |
dc.title | Optimal boundary control of a viscous Cahn-Hilliard system with dynamic boundary condition and double obstacle potentials | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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