题目：Time fractional equations and probabilistic representation
报告人：陈振庆
时 间：2018年8月11日16：00-17：00
地 点：3-309
报告人简介：陈振庆，美国华盛顿大学（西雅图）数学系教授、国家“千人计划”特聘专家、“长江学者奖励计划”讲座教授，曾任北京理工大学数学科学学院院长。陈振庆教授是国际顶级期刊《The Annals of Probability》的副主编，国际权威期刊《Potential Analysis》的主编，《Proceedings of the American Mathematical Society》、《Journal of Theoretical Probability》、《Probability, Uncertainty and Quantitative Risk》编委。 曾任国际权威期刊《The Annals of Applied Probability》、《Stochastic Processes and their Application》、《Electronic Communications in Probability》、《Journal of Applied Mathematics and Computing》、《中国科学》等众多期刊的副主编或编委。 陈振庆教授1992年在美国华盛顿大学（圣路易斯）获博士学位，曾在美国的加利福尼亚大学（圣地亚哥）和康奈尔大学工作；1998年起在位于华盛顿州西雅图市的华盛顿大学数学系工作至今。主要从事概率论及随机过程的研究，主要研究方向是：随机分析，随机微分方程，马氏过程及其位势理论，狄氏型，发表论文160余篇。
个人主页：https://sites.math.washington.edu/~zchen/
Abstract: Time-fractional diffusion equations have been actively studied in several fields including mathematics, physics, chemistry, engineering, hydrology and even finance and social sciences as they can be used to model the anomalous diffusions exhibiting subdiffusive behavior, due to particle sticking and trapping phenomena. In this talk, I will report some recent progress in the study of general fractional-time parabolic equations of mixture type, including existence and uniqueness of the solutions and their probabilistic representations in terms of the corresponding inverse subordinators with or without drifts. Sharp two-sided estimates on the fundamental solution will be given .Fractional -time parabolic equations with source term will also be discussed. In particular, a new representation formula for the solution of time fractional Poisson equation will be presented, which does not involve fractional time derivative of the fundamental solution.
