Fractional partial differential equations for ultra-slow diffusion: analysis and computation

报告题目：Fractional partial differential equations for ultra-slow diffusion: analysis and computation

报告时间：2023年10月20日下午16:00-17:00

报告地点：红瓦楼726

报告人：李常品 教授（上海大学）

报告摘要：The known ultra-slow diffusion indicates that the diffusion rate is algebraic in the sense of logarithmic function. Such a kind of diffusions is often modeled by the fractional Hadamard derivatives. In this talk, we first introduce the various kinds of numerical algorithms for Caputo-Hadamard derivatives. Then we apply the derived algorithms to long term integration of the typical fractional differential equations, such as the fractional Lorenz system, the Bagley-Torvik system, and the fractional Allen-Cahn equation, with Caputo-Hadamard derivatives. Last we theoretically and numerically study the finite blow-up solutions of the semi-linear fractional partial differential equations with Caputo-Hadamard derivatives.

报告人简介：上海大学数学系教授、博士生导师、伟长学者、英国IMA会士(FIMA, Fellow of the Institute of Mathematics and its Applications, UK)。2021年获上海大学王宽诚育才奖，2017年和2010年获上海市自然科学奖，2016年入选上海市优秀博士学位论文指导教师，2012年获分数阶微积分领域的黎曼-刘维尔理论文章奖，2011年获宝钢优秀教师奖。主要研究方向为分数阶偏微分方程数值解。在SIAM和Chapman and Hall/CRC出版专著各1部，在World Scientific编辑专著1部；发表SCI论文140余篇。主持国家自然科学基金、上海市教委科研创新重点基金等科研项目10余项，主持上海市教委本科重点课程建设等教改项目4项。德国德古意特出版社系列丛书《Fractional Calculus in Applied Sciences and Engineering》创始主编，Appl. Numer. Math., Fract. Calc. Appl. Anal., J Nonlinear Sci., Math Computer Simulation, Math. Meth. Appl. Sci.等杂志编委或顾问编委。

报告邀请人：盛长滔，刘欢 博士