Optimal Distributed Control of a Cahn-Hilliard-Darcy System with Mass Sources
Abstract
In this paper, we study an optimal control problem for a two-dimensional Cahn-Hilliard-Darcy 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 Fr\'echet 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
Cite
@article{arxiv.1809.09037,
title = {Optimal Distributed Control of a Cahn-Hilliard-Darcy System with Mass Sources},
author = {Juergen Sprekels and Hao Wu},
journal= {arXiv preprint arXiv:1809.09037},
year = {2023}
}