活动时间：2023-11-09 18:00

活动地点：Zoom Meeting ID: 815 3266 3954  Passcode: 008040

主讲人：邵崇哲

主讲人中文简介：

邵崇哲老师现任英国伦敦玛丽女王大学数学科学学院 Reader （副教授），其于普林斯顿大学获得博士学位，博士导师是著名数学家 Sergiu Klainerman, 后曾在多伦多大学和伦敦帝国理工学院工作，是偏微分方程、微分几何以及广义相对论等方面的专家，其研究工作发表于 JEMS、CMP、ARMA、Adv. Math、TAMS、PLMS 、JFA 、CPDE 等权威数学杂质。

活动内容摘要：

We consider heat operators on a bounded domain, with a critically singular potential diverging as the inverse square of the distance to the boundary of the domain. We establish the first boundary controllability results for such operators in all spatial dimensions.

For the first result, we prove null controllability when the domain is also convex, and with control imposed on the entire boundary. The key step in the proof is a sum of novel global Carleman estimates that captures both the relevant boundary asymptotics and the appropriate energy. Next, we prove approximate controllability, but without any assumption of convexity, and with the control localised to an arbitrarily small neighborhood. The key step is a local Carleman estimate and unique continuation property.

This is joint work with Alberto Enciso (ICMAT) and Bruno Vergara (Brown).

主持人：查冬兵