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报告题目：Analysis and simulation of optimal control for a two-time-scale fractional advection-diffusion-reaction equation

报告人：   郑祥成，山东大学，研究员

报告时间：2023年11月20日上午九点

报告地点：江宁校区励学楼B327

邀请人：   郭英文

报告摘要：We investigate an optimal control model with pointwise constraints governed by a two-time-scale time-fractional advection-diffusion-reaction equation with space-time dependent fractional order and coefficients, which describes, e.g., the contaminant in groundwater under various transport scales or miscible displacement of hydrocarbon by injected fluid through heterogeneous porous media. To accommodate the effects of complex fractional order and coefficients, an auxiliary equation method is proposed, along with the Fredholm alternative for compact operators, to analyze the well-posedness of the state equation. Additionally, a bootstrapping argument is utilized to progressively improve the solution regularity, leading to the maximal regularity estimates. Subsequently, we analyze the adjoint equation derived from the first-order optimality condition. Based on these findings, we ultimately analyze the well-posedness, first-order optimality conditions and maximal regularity estimates for the optimal control problem, and conduct numerical experiments to investigate its behavior in potential applications。

 报告人简介：郑祥成，齐鲁青年学者，主要从事非线性问题多解算法和解景观方法、非局部偏微分方程和积分方程的理论与数值分析等方面的研究，近五年在SIAM系列、Inverse Problems、CMAME、IMAJNA、JCP等计算与应用数学权威期刊发表SCI论文80余篇，担任SISC等40余种SCI期刊的审稿人，主持国家自然科学基金、中国博士后国际交流引进项目和中国博士后科学基金等，入选山东省“泰山学者”青年专家和中国工业与应用数学学会“青年人才托举工程”。