報告題目：Analysis and simulation of optimal control for a two-time-scale fractional advection-diffusion-reaction equation

報告人：   鄭祥成，山東大學，研究員

報告時間：2023年11月20日上午九點

報告地點：江甯校區勵學樓B327

邀請人：   郭英文

報告摘要：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。

 報告人簡介：鄭祥成，齊魯青年學者，主要從事非線性問題多解算法和解景觀方法、非局部偏微分方程和積分方程的理論與數值分析等方面的研究，近五年在SIAM系列、Inverse Problems、CMAME、IMAJNA、JCP等計算與應用數學權威期刊發表SCI論文80餘篇，擔任SISC等40餘種SCI期刊的審稿人，主持國家自然科學基金、中國博士後國際交流引進項目和中國博士後科學基金等，入選山東省“泰山學者”青年專家和中國工業與應用數學學會“青年人才托舉工程”。