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MATHEMATICAL MODELING AND NUMERICAL ANALYSIS OF ANOMALOUS DIFFUSION
时间:2017-07-13 14:58    点击:   所属单位:数学与统计学院
讲座名称 MATHEMATICAL MODELING AND NUMERICAL ANALYSIS OF ANOMALOUS DIFFUSION
讲座时间 2017-07-20 10:30:00
讲座地点 信远楼II205
讲座人 周知博士
讲座人介绍 周知博士,从事偏微分方程的数值计算、分数阶偏微分方程、科学计算、反问题与最优控制等研究工作。20102015年在美国德州农工大学 (Texas A&M University)读博士,20158月—20175月在美国哥伦比亚大学 (Columbia University) 应用物理与应用数学系读博士后,现在香港理工大学(Hong Kong Polytechnic University)应用数学系任助理教授。已在“SIAM J. Numer. Anal.”“IMA J. Numer. Anal.”“J. Compt. Phy.”“Numer. Math.,”“SIAM J. Sci. Comput.”等国际知名期刊上发表学术论文20多篇,其中有两篇论文在20142015年的IMA NUM 中高被引论文中排前10.
讲座内容

Anomalous diffusion has received much attention in recent years. It describes a diffusion process in which the mean square displacement of a particle grows faster (super-diffusion) or slower (sub-diffusion) than that in the normal diffusion process. In analogy with Brownian motion for normal diffusion, anomalous diffusion is the macroscopic counterpart of continuous time random walk. To begin with, I will introduce the anomalous diffusion and its wide applications. Next, as a typical example, the time-fractional diffusion (sub-diffusion) will be studied. The nonlocality of the fractional derivative appearing in the model changes dramatically the behavior of solution and hence leads to some computational challenges. Our aim is to develop effcient numerical schemes which are robust with respect to nonsmooth data, and to verify its convergence rate theoretically. I will present novel strategies to overcome these diffculties. Finally, a general nonlocal diffusion model will be proposed to study the crossover of various diffusive regimes that has been widely observed in practice. It has a finite-memory effect and transient behavior, and bridges the normal local diffusion and the fractional diffusion.

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