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Application of fixed point-collocation method for solving an optimal control problem of a parabolic-hyperbolic free boundary problem modeling the growth of tumor with drug application

机译:定点配置方法在求解药物生长模拟抛物线-双曲线自由边界问题的最优控制问题中的应用

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In this paper, employing a fixed point-collocation method, we solve an optimal control problem for a model of tumor growth with drug application. This model is a free boundary problem and consists of five time-dependent partial differential equations including three different first-order hyperbolic equations describing the evolution of cells and two second-order parabolic equations describing the diffusion of nutrient and drug concentration. In the mentioned optimal control problem, the concentration of nutrient and drug is controlled using some control variables in order to destroy the tumor cells. In this study, applying the fixed point method, we construct a sequence converging to the solution of the optimal control problem. In each step of the fixed point iteration, the problem changes to a linear one and the parabolic equations are solved using the collocation method. The stability of the method is also proved. Some examples are considered to illustrate the efficiency of method. (C) 2017 Elsevier Ltd. All rights reserved.
机译:在本文中,采用定点配置方法,我们解决了应用药物的肿瘤生长模型的最优控制问题。该模型是一个自由边界问题,由五个与时间有关的偏微分方程组成,其中包括三个不同的描述细胞演化的一阶双曲方程和两个描述营养素和药物浓度扩散的二阶抛物方程。在所提到的最佳控制问题中,使用一些控制变量来控制营养物和药物的浓度,以破坏肿瘤细胞。在这项研究中,应用定点方法,我们构造了一个收敛于最优控制问题解的序列。在定点迭代的每个步骤中,问题都变为线性方程,并且使用搭配方法求解抛物线方程。还证明了该方法的稳定性。考虑一些例子来说明方法的效率。 (C)2017 Elsevier Ltd.保留所有权利。

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