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.

Speaker's profile: Associate Professor at the Center for Applied Mathematics, Tianjin University. I obtained my doctoral degree from Wuhan University in 2017 and will conduct Humboldt Scholar research in Germany from 2023 to 2024. The main research direction is the control theory of distributed parameter systems, especially in the controllability of the Schr ö dinger equation and the observability of the heat equation with memory. Breakthrough progress has been made, and related research results have been published in internationally renowned journals such as JEMS, JMPA, ARMA, SICON, etc.