Optimal distributed control of a diffuse interface model of tumor growth
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2228 | |
dc.contributor.author | Colli, Pierluigi | |
dc.contributor.author | Gilardi, Gianni | |
dc.contributor.author | Rocca, Elisabetta | |
dc.contributor.author | Sprekels, Jürgen | |
dc.date.accessioned | 2016-12-13T10:46:57Z | |
dc.date.available | 2019-06-28T08:01:56Z | |
dc.date.issued | 2016 | |
dc.description.abstract | In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed by HawkinsDaruud et al. in [25]. The model consists of a CahnHilliard equation for the tumor cell fraction 'coupled to a reaction-diffusion equation for a function phi representing the nutrientrich extracellular water volume fraction. The distributed control u monitors as a right-hand side the equation for sigma and can be interpreted as a nutrient supply or a medication, while the cost function, which is of standard tracking type, is meant to keep the tumor cell fraction under control during the evolution. We show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive the first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2919 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1635 | |
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 | Distributed optimal control | eng |
dc.subject.other | first-order necessary optimality conditions | eng |
dc.subject.other | tumor growth | eng |
dc.subject.other | reaction-diffusion equations | eng |
dc.subject.other | Cahn–Hilliard equation | eng |
dc.title | Optimal distributed control of a diffuse interface model of tumor growth | 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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