学术报告: Unique continuation principle for the two dimensional time fractional diffusion equation
发布时间: 2019-12-25  浏览次数: 10

河海大学理学院学术报告系列

——应用偏微分方程小组Seminar

报告题目:    Unique continuation principle for the two dimensional time fractional diffusion equation

报告人:       李志远 副教授

报告人单位:  山东理工大学

报告日期:    20191226日 星期四

报告时间:    9:30-10:30

报告地点:    江宁校区励学楼 B110

邀请人:      程 星

欢迎广大师生参加。    

摘要In this talk, the diffusion equation with Caputo derivative is discussed. The Caputo derivative is inherently nonlocal in time with history dependence, which makes the crucial differences between fractional models and classical models, for example, long-time asymptotic behavior. However, a maximum principle in the usual setting still holds. Is there any other property retained from the parabolic equations? What about the unique continuation (UC)? There is not affirmative answer to this problem except for some special cases. Sakamoto-Yamamoto (2011) asserted that the vanishment of a solution to a homogeneous problem in an open subset implies its vanishment in the whole domain provided the solution vanishes on the whole boundary. Lin-Nakamura (2016) obtained a UC by using a Carleman estimate providing the homogeneous initial value. Both of these results are called as the weak UC because the homogeneous condition is imposed on the boundary value or on the initial value, which is absent in the parabolic prototype. In this talk, by using Phragmen-Lindelof principle and Laplace transform argument, we will give a classical type unique continuation.

报告人简介: 李志远,山东理工大学数学与统计学院副教授,2015年博士毕业于东京大学,并且在东京大学从事两年博士后研究工作。李志远博士主要从事偏微分方程反问题的研究工作,特别是奇异介质中的异常扩散过程以及与之对应的分数阶反应扩散方程的研究工作。在Inverse Problems,Fractional Calculus and Applied Analysis等国际著名期刊发表论文18篇,他引用次数90次。他的研究成果受到国际同行的高度评价和认可。他于2016年获得JSPS 博士后基础研究经费,目前正在主持国家自然科学基金青年基金项目。