珠海数学杰出学者讲座第50讲-Periodic propagation of singularities for heat equations with time delay

讲座题目：Periodic propagation of singularities for heat equations with  time delay
讲座时间 Datetime: 2025年4月29日，周二，15:00-17:15
地点 Venue: 中大珠海校区海琴二号A457/腾讯会议 604-830-884               
主持人 Host：黄山林 副教授
报告人 Speaker: 汪更生 教授
单位 Affiliation: 天津大学
报告摘要 Abstract:
This talk presents two phenomena for the heat equation with a time delay: the propagation of singularities and the periodicity. These are reflected in a special propagation of singularities of solutions. That is, the singularities of the solutions periodically propagate in the time direction in a bidirectional manner. Moreover, the propagation is stepped. Specifically, when propagated along the positive time direction, the order of the joint derivatives of the solution increases by 2 per period; whereas when propagated in the reverse direction, the order of the joint derivatives decreases by 2 per period. We also show how the initial data and historical values affect such a propagation of singularities.The phenomena we observed not only confirm the significant differences between heat equations with and without time delay but also demonstrate the substantial difference between the heat equation with a time delay and the wave equation, from the perspective of propagation of singularities.This is a joint work with Huaiqiang Yu and yubiao Zhang.
报告人简介：
汪更生，天津大学应用数学中心教授，新世纪百千万人才国家级人选；主要研究分布参数系统控制理论，在偏微分方程的能控能观性、能稳性和时间最优控制等方向有杰出贡献，并受邀在2026年国际数学家大会作45分钟报告；现任控制领域顶刊SIAM J. Control and Optimization和数学控制论顶刊ESAIM: Control Optim. Calc. Var.等的编委。