报告题目：Observability inequality, log-type Hausdorff content and heat equations

报告人：汪更生 教授 天津大学

报告时间：2025年7月7日10：00-11：00

报告地点：数学楼一楼第一报告厅

报告摘要：This paper studies the observability inequality for heat equations defined on a bounded domain of $\R^d$ and the whole space $\R^d$ respectively, where the observation sets are measured by a Hausdorff content, defined by a log-type gauge function, which is closely related to the heat kernel. For the heat equation on a bounded domain, we obtain the observability inequality for observation sets of positive log-type Hausdorff content, which, in particular, implies the observability inequality for observation sets of positive s-dim Hausdorff measure, where s can be any number in $(d-1,d]$. For the heat equation over $\R^d$, we build up the observability inequality for observation sets which are thick at scale of the log-type Hausdorff content.

This is a recent work joint with Shanlin Huang and Ming Wang.

报告人简介： Gengsheng Wang is a professor at the Center for Applied Mathematics, Tianjin University, P.R. China. He earned his Ph.D. from Ohio University in 1994, and his M.S. and B.S. degrees from Wuhan University in 1986 and 1983, respectively. He served as a professor at Central China Normal University from 1996 to 2004, and at Wuhan University from 2005 to 2017. He is an internationally renowned expert in PDE control, specializing in the control theory of distributed parameter systems. His research focuses on the controllability, observability, stabilizability, and time-optimal control of PDEs. In particular, he has made significant contributions to the observability inequalities of the heat equation and the Schrödinger equation. He currently serves on the editorial boards of SIAM Journal on Control and Optimization, ESAIM: Control, Optimisation and Calculus of Variations, and Mathematical Control and Related Fields. He was invited to give a 45-minute talk at the 2026 International Congress of Mathematicians.