Well-posedness and optimal control for a Cahn--Hilliard--Oono system with control in the mass term
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2867 | |
dc.contributor.author | Colli, Pierluigi | |
dc.contributor.author | Gilardi, Gianni | |
dc.contributor.author | Rocca, Elisabetta | |
dc.contributor.author | Sprekels, Jürgen | |
dc.date.accessioned | 2022-07-05T14:28:47Z | |
dc.date.available | 2022-07-05T14:28:47Z | |
dc.date.issued | 2021 | |
dc.description.abstract | The paper treats the problem of optimal distributed control of a Cahn--Hilliard--Oono system in Rd, 1 ≤ d ≤ 3 with the control located in the mass term and admitting general potentials that include both the case of a regular potential and the case of some singular potential. The first part of the paper is concerned with the dependence of the phase variable on the control variable. For this purpose, suitable regularity and continuous dependence results are shown. In particular, in the case of a logarithmic potential, we need to prove an ad hoc strict separation property, and for this reason we have to restrict ourselves to the case d = 2. In the rest of the work, we study the necessary first-order optimality conditions, which are proved under suitable compatibility conditions on the initial datum of the phase variable and the time derivative of the control, at least in case of potentials having unbounded domain | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9585 | |
dc.identifier.uri | https://doi.org/10.34657/8623 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2867 | |
dc.relation.hasversion | https://doi.org/10.3934/dcdss.2022001 | |
dc.relation.issn | 2198-5855 | |
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 | |
dc.subject.other | Cahn--Hilliard equation | eng |
dc.subject.other | logarithmic potential | eng |
dc.subject.other | regular potential | eng |
dc.subject.other | optimal control problem | eng |
dc.subject.other | strict separation property | eng |
dc.subject.other | necessary optimality conditions | eng |
dc.title | Well-posedness and optimal control for a Cahn--Hilliard--Oono system with control in the mass term | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 38 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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