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Title: Optimal distributed control of a Cahn-Hilliard-Darcy system with mass sources
Authors: Sprekels, JürgenWu, Hao
Publishers Version: https://doi.org/10.20347/WIAS.PREPRINT.2548
Issue Date: 2018
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2548, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: In this paper, we study an optimal control problem for a two-dimensional CahnHilliardDarcy system with mass sources that arises in the modeling of tumor growth. The aim is to monitor the tumor fraction in a finite time interval in such a way that both the tumor fraction, measured in terms of a tracking type cost functional, is kept under control and minimal harm is inflicted to the patient by administering the control, which could either be a drug or nutrition. We first prove that the optimal control problem admits a solution. Then we show that the control-to-state operator is Fréchet differentiable between suitable Banach spaces and derive the first-order necessary optimality conditions in terms of the adjoint variables and the usual variational inequality.
Keywords: Cahn–Hilliard–Darcy system; distributed optimal control; necessary optimality condition
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.
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Appears in Collections:Mathematik



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