Aiguo Xiao, Professor, Xiangtan University

Yifa Tang, Professor

Space-Fractional Diffusion Equation with Variable Coefficients: Well-posedness and Fourier Pseudospectral Approximation

9:30-10:30 September 9 (Saturday), N702

Multi-dimensional space-fractional diffusion equation with variable coefficients and fractional gradient is a difficult problem in theory and computation. As far as we know, there rarely exist well-posedness results and efficient numerical approaches for such equation. In this talk, we focus on this subject. First, we apply the commutator estimation method to prove the coercivity of the non-positive bilinear form for such equation in both continuous and discrete senses, and this is key for the later discussion. Then, we prove the well-posedness of the analytical solution and give the global error estimation of the numerical solution obtained by Crank-Nicolson Fourier pseudospectral scheme. Last, the numerical experiments are used to verify the main results of the theoretical analysis, and a model for the plume of solute through groundwater is exhibited to show the application of space-fractional diffusion theory.

报告人简介：1999年在北京应用物理与计算数学研究所获理学博士学位，2001年从中国科学院计算数学与科学工程计算研究所博士后出站。现任湘潭大学数学与计算科学学院教授、湘潭大学韶峰学者特聘岗位学科带头人、湖南省级重点实验室主任、《数值计算与计算机应用》编委、中国仿真学会仿真算法专业委员会主任委员等。长期从事微分方程数值方法研究，主持国家863课题和国家自然科学基金面上项目6项等，发表SCI论文80多篇，获教育部和湖南省自然科学二等奖、国家教学成果二等奖、湖南省教学成果一等奖、宝钢教育奖优秀教师奖、湖南省优秀研究生导师等。