报告题目：Recent progress in coupled systems and semilinear problems of time-fractional diffusion equations
报 告 人：刘逸侃（京都大学）
会议时间：2024年01月03 下午15:30开始
会议地点：包玉书9号楼113报告厅
报告摘要：The last decade has witnessed explosive developments and gradual saturation of nonlocal models from various practical backgrounds. As a popular representative, partial differential equations with fractional derivatives in time have gathered considerable attentions among applied mathematicians. Recently, linear theory for fractional diffusion equations with time derivatives in (0,1) has been well established, followed by extensive researches on related numerical methods and inverse problems. This motivates the generalizations of studies from single equations to coupled systems and from linear to nonlinear problems.
Started with a brief survey on existing results on time-fractional partial differential equations, this talk is concerned with the solution dynamics of their coupled and semilinear counterparts. For coupled time-fractional diffusion systems, we obtain a sharp estimate for the long-time asymptotic behavior of solutions by the Laplace transform. Further, we discover a new decay pattern by the coupling of non-fractional and fractional diffusion equations. For time-fractional diffusion equation with superlinear convex semilinear term, we show the blow-up of solutions and provide upper estimates of the blow-up times by a comparison principle.
报告人简介：刘逸侃博士，现任日本京都大学大学院理学研究科副教授。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，从2019年起任北海道大学电子科学研究所助理教授，于2023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偏微分方程的性质及其对反问题的应用。现已发表SCI论文近30篇，翻译专著1册，MathSciNet和Google Scholar上分别被引用逾480次和1070次。
