Time-fractional diffusion equations and a related parameter inverse problem with inexact data
刘逸侃 助理教授
北海道大学
报告时间：2022年11月08日19:00
报告地点：腾讯会议：576-338-238
报告摘要：Recently, linear theories for time-fractional diffusion equations have been well established and related inverse problems have been studied intensively. Among many similarities with usual parabolic equations, they show essential difference in the slow decay depending on the order of time derivatives, which has been applied to determining orders and parameters. In literature, uniqueness for such inverse problems was proved with coinciding data, but there seems no stability result with noisy data. Only using initial inexact data at a single point, in this research we obtained uniqueness for determining orders and parameters simultaneously with unknown initial values, which is stronger than stability. Further, in some special case we can even conclude the uniqueness of initial values. The proof relies on the asymptotic expansion after taking the Laplace transform and the completeness of generalized eigenfunctions. This is a joint work with Masahiro Yamamoto (The University of Tokyo).
报告人简介：刘逸侃博士，现任日本北海道大学电子科学研究所助理教授。他自2011年起师从东京大学大学院数理科学研究科山本昌宏（Masahiro Yamamoto）教授，于2015年获得博士学位（数理科学）。之后他在东京大学历任特任研究员、日本学术振兴会外国人特别研究员和特任助教，于2019年就任现职。他的研究方向为偏微分方程的反问题，主要包括双曲型方程、时间分数阶发展方程和静弹性体方程反问题的理论唯一性、稳定性以及数值反演，近年主要研究时间分数阶扩散和波动方程的性质及其对反问题的应用。现已发表SCI论文20余篇，翻译专著1册，MathSciNet和Google Scholar上分别被引用逾350次和860次。