SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1555-1580, January 2021.
In this paper, we study an optimal control problem for a macroscopic mechanical tumor model based on the phase field approach. The model couples a Cahn--Hilliard-type equation to a system of linear elasticity and a reaction-diffusion equation for a nutrient concentration. By taking advantage of previous analytical well-posedness results established by the authors, we seek optimal controls in the form of a boundary nutrient supply as well as concentrations of cytotoxic and antiangiogenic drugs that minimize a cost functional involving mechanical stresses. Special attention is given to sparsity effects, where with the inclusion of convex nondifferentiable regularization terms to the cost functional, we can infer from the first-order optimality conditions that the optimal drug concentrations can vanish on certain time intervals.

中文翻译：

---

具有机械效应的相场肿瘤模型的稀疏最优控制

SIAM控制与优化杂志，第59卷，第2期，第1555-1580页，2021年1月。
在本文中，我们基于相场方法研究了宏观机械肿瘤模型的最优控制问题。该模型将Cahn-Hilliard型方程式与线性弹性系统和营养物浓度的反应扩散方程式耦合。通过利用作者先前建立的分析性定性结果，我们以边界营养物供应以及细胞毒性和抗血管生成药物浓度的形式寻求最佳控制，以最大程度地降低涉及机械应力的功能成本。特别注意稀疏效应，其中在成本函数中包含凸不可微正则化项，我们可以从一阶最优性条件推断出最佳药物浓度可以在特定时间间隔内消失。