报告时间：2021年5月7日下午16：00-17：00

报告地点：龙洞校区教学楼313

报告人：李常品 教授 上海大学数学科学学院

主持人：汪志波

报告题目：Non-uniform L1/LDG method for the Caputo-Hadamard fractional partial differential equation

报告摘要：In this talk, we introduce the Caputo–Hadamard fractional partial differential equation where the time derivative is the Caputo–Hadamard fractional one and the space derivative is theinteger-order one. We first present a modified Laplace transform. Then using the newly defined Laplace transform and the well-known finite Fourier sine transform, we obtain the analytical solution to this kind of linear equation. Furthermore, we study the regularity and logarithmic decay of its solution. Since the equation has a time fractional derivative, its solution behaves a certain weak regularity at the initial time. We use the finite difference scheme on non-uniform meshes to approximate the time fractional derivative in order to guarantee the accuracy, and use the local discontinuous Galerkin method (LDG) to approximate the special derivative. The fully discrete scheme is established and analyzed. A numerical example is displayed which support the theoretical analysis.

专家简介：李常品，博士、上海大学数学系教授、博士生导师。主要研究方向为分数阶偏微分方程数值解、分岔混沌的应用理论和计算。在Journal of Computational Physics, Journal of Nonlinear Science, Journal of Scientific Computing, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing等期刊上发表论文140余篇，在SIAM等出版社出版专著2部。自2018年，连续入选科睿唯安“全球高被引科学家”。是德国德古意特出版社系列丛书《Fractional Calculus in Applied Sciences and Engineering》的创始主编，是Applied Numerical Mathematics, Chaos, Fractional Calculus and Applied Analysis, Mathematics and Computers in Simulations, 《上海大学学报(自然科学版)》等杂志编委。2017年和2010年两次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。