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Title: Optimal distributed control of a diffuse interface model of tumor growth
Authors: Colli, PierluigiGilardi, GianniRocca, ElisabettaSprekels, Jürgen
Issue Date: 2016
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2228, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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.
Keywords: Distributed optimal control; first-order necessary optimality conditions; tumor growth; reaction-diffusion equations; Cahn–Hilliard equation
DDC: 510
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.
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.
Appears in Collections:Mathematik

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