报告题目: Unique continuation principle for the time-fractional diffusion equation
报告人： 李志远 博士
报告人单位：山东理工大学
报告时间：2018年11月28日,下午16:00-17:00
报告地点：数学学院第一报告厅
报告摘要:
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 equationsWhat 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 Theta function method and Laplace transform argument, we will give a classical type unique continuation.
报告人介绍：
李志远，山东理工大学数学与统计学院副教授，博士毕业于东京大学，主要从事反问题的研究工作，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8篇，引用次数72次（MathSciNet）。目前主持国家自然科学基金青年基金项目“分数阶扩散方程中几类反问题的理论分析与反演算法研究”。