报告题目： An optimal control of a variable-order fractional PDE
报 告 人：王宏 教授 （University of South Carolina南卡罗莱纳大学）
邀 请 人：宋怀玲
报告时间：2023/05/16 周二 上午 10:00-11:30
报告地点：腾讯会议
会 议 号：855-914-449（无密码）
摘 要：
Fractional diffusion PDEs were derived assuming their solutions have power-law decaying tails, and so accurately model diffusive transport in heterogeneous aquifers. However, fractional PDEs introduce new modeling, computational and mathematical issues that are not common in the context of integer-order PDEs. In this talk we will go over these issues and focus on the discussion of modeling issues. If time permits, we will also discuss mathematical, numerical, and computational issues and report recent progress in these directions.
The variable-order optimal control encounters mathematical and numerical issues that are not common in its integer-order and constant-order fractional analogues: (i) The adjoint state equation of the variable-order Caputo time-fractional PDE turns out to be a different and more complex type of variable-order Riemann-Liouville time-fractional PDE. (ii) The coupling of the variable-order fractional state PDE and adjoint state PDE, and the variational inequality reduces the regularity of the solution to the optimal control. (iii) The numerical approximation to fractional optimal control model needs to be analyzed due to the low regularity and coupling of the model. We will prove the wellposedness and regularity of the model and an optimal-order error estimate to its numerical discretization.
报告人简介：美国南卡罗来纳大学数学系终身教授，山东省泰山学者海外特聘教授。分别于1982年和1984年获山东大学数学学士学位和计算数学硕士学位，1992年获美国怀俄明大学数学博士学位。主要研究方向为数值分析、大规模科学计算、数值模拟以及整数阶和分数阶偏微分方程的应用方面的研究。迄今为止已在国际知名期刊SIAM J Numer. Anal.、 SIAM J Sci. Comput.、 J Comput Phys、和IMA J. Numer. Anal.等国际权威学术杂志发表论文百余篇。王宏教授还是Numer. Methods PDEs、Computing and Visualization in Sciences和Int J. Numer. Anal. Modeling等国际知名杂志的编委。
欢迎感兴趣的老师和同学们参加！
