In this talk, we first introduce the propagation of singularities for solutions to heat equations with memory in lower-order terms. We then establish a two-sided observability inequality that enables quantitative reconstruction of a solution's initial data from partial measurements. This is accompanied by: (i) characterization of the geometric condition on observable regions, (ii) relation to the aforementioned propagation phenomenon.

报告人简介：天津大学应用数学中心副教授。2017年在武汉大学取得博士学位，2023-2024年在德国做洪堡学者研究。主要研究方向是分布参数系统的控制理论，特别是在薛定谔方程的能控性、带记忆热方程的能观性等取得了突破性的进展，相关研究成果先后发表在JEMS, JMPA, ARMA, SICON等国际著名期刊。