国家天元数学东北中心将于2022年3月1日-4月2日在举办“Numerical Treatment and Analysis of Time-Fractional Evolution Equations”线上短课。该课程由香港理工大学周知助理教授开授，旨在为从事该领域研究的青年教师和研究生提供系统性讲解。

一、课程基本信息

1、授课人：周知 助理教授

2、授课人单位：香港理工大学

3、课程名称：Numerical Treatment and Analysis of Time-Fractional Evolution Equations

4、开课时间段：2022年3月1日-4月2日

5、预备知识：偏微分方程，数值分析的基础知识。

6、所需教材：自编

7、课程形式：腾讯会议

会议账号（周二）：804-6553-8257

会议账号（周六）：863-1186-1959 

二、课程介绍

Fractional differential equations, one important class of nonlocal models, have received much recent attention in physics, biology and mathematics, due to their extraordinary modeling capability for describing certain anomalous transport phenomena observed in real world. The fractional operators involved in those models may significantly change both diffusive dynamics and solution regularity. The aim of this short course is to provide insight in the mathematics of numerical methods for solving time-fractional evolution equations.

The short course will cover the following contents:

1. Introduction to fractional calculus, time-fractional subdiffusion models, and relevant solution theory.

2. Semidiscrete schemes by finite element methods.

3. Time stepping schemes by convolution quadrature.

4. Time stepping schemes by piecewise polynomial interpolation.

5. Discrete fractional maximal regularity.

6. Subdiffusion with time-dependent coefficients.

7. Semilinear subdiffusion equations.

8. Space-time formulation and spectral methods.

9. Optimal control with subdiffusion constraint.

10. Backward problems for subdiffusion. 

三、授课人介绍

Zhi Zhou received his B.Sc in computational mathematics in 2010 from Nanjing University of Aeronautics and Astronautics, and the Ph.D. degree in mathematics from Texas A&M University. During 2015-2017, he was a postdoctorial scientist at the Department of Applied Physics and Applied Mathematics, Columbia University. Currently, he is an Assistant Professor at the Department of Applied Mathematics, Hong Kong Polytechnic University. His research interests lie primarily in the fields of numerical PDEs, scientific computing, nonlocal/fractional models, and inverse problems.

授课人照片：

四、联系方式

若您对该门课程感兴趣，欢迎联系我们！

办公电话：0431-85167375

邮箱：tianyuanmath@jlu.edu.cn

地址：吉林大学数学学院315办公室