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arXiv · 1809.09037

Optimal Distributed Control of a Cahn-Hilliard-Darcy System with Mass Sources

Juergen Sprekels·Hao Wu
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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.

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Juergen Sprekels, Hao Wu. 2018-09-24. Optimal Distributed Control of a Cahn-Hilliard-Darcy System with Mass Sources. https://doi.org/10.1007/s00245-019-09555-4

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