Numerical Optimal Control of a Size-Structured PDE Model for Metastatic Cancer Treatment
报告题目： Numerical Optimal Control of a Size-Structured PDE Model for Metastatic Cancer Treatment
报告时间：2019年7月8日，星期一，下午 17:20-18:20
报告地点：数学楼2-3会议室
报告人: Dr. Wang Xiangsheng，University of Louisiana at Lafayette
Abstract:
We propose a unified size-structured PDE model for the growth of metastatic tumors, which extends a well-known coupled ODE-PDE dynamical model developed and studied in the literature. A treatment model based on the proposed unified PDE model is investigated via optimal control theory, where its first-order necessary optimality system characterizing the optimal control is derived. We prove that the uniqueness of the optimal control depends on the chosen objective functional, and the optimal control is of bang-bang type when it is unique. For obtaining its efficient numerical solutions, a projection gradient descent algorithm based on the characteristic scheme is developed for solving the established optimal treatment model. Several numerical examples are provided to validate our mathematical analysis and numerical algorithm, and also illustrate the biologically interesting treatment outcomes of different models and control strategies. Our simple model reveals that: (i) only the total drug dosage matters if one just cares about the final treatment output; (ii) given the same total drug dosage, the optimal bang-bang treatment plan outperforms the others in the sense that it maximally reduces the total tumor sizes during the whole period of treatment, although their final tumor sizes are the same.
报告人简介 ：
汪翔升博士2004年毕业中国科技大学数学系，获学士学位；于2009年获得香港城市大学博士学位；2009-2013年先后在香港城市大学，加拿大York大学、Memorial University of Newfoundland大学从事博士后研究工作，现在任职于美国University of Louisiana at Lafayette大学，主要研究渐近分析、微分动力系统、生物数学和计算数学。迄今为止已在Advances in Mathematics、SIAM Journal on Control and Optimization、Journal of Differential Equations、Analytical Chemistry、Physics Review E、Proceedings of the American Mathematical Society 、 Studies in Applied Mathematics、Journal of Dynamics and Differential Equations、Journal of Theoretical Biology、Statistica Sinica等国际期刊上发表学术论文三十余篇。汪翔升博士是路易斯安那大学拉法叶分校数学专业博士研究生的招生负责人。
