论文标题
对具有机械效应的相位场肿瘤模型的稀疏最佳控制
Sparse optimal control of a phase field tumour model with mechanical effects
论文作者
论文摘要
在本文中，我们研究了基于相场方法的宏观机械肿瘤模型的最佳控制问题。该模型将Cahn--Hilliard类型方程式融合到线性弹性系统和营养浓度的反应扩散方程。通过利用作者建立的先前的分析良好的结果，我们寻求以边界营养供应形式的最佳控制，以及浓度的细胞毒性和抗血管生成药物，以最大程度地减少涉及机械应力的成本功能。特别注意稀疏性效应，其中包含凸的非差异正则化术语到成本功能，我们可以从一阶最佳条件中推断出最佳药物浓度可以在一定时间间隔中消失。
In this paper, we study an optimal control problem for a macroscopic mechanical tumour 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 minimise a cost functional involving mechanical stresses. Special attention is given to sparsity effects, where with the inclusion of convex non-differentiable regularisation 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.
