Observability inequality, log-type
Hausdorff content and heat equations
报告专家：汪更生教授（天津大学）
报告时间：2025年4月17日（星期四）下午4:00-5:00
报告地点：国家天元数学西南中心516报告厅
报告摘要：This talk introduces the observability inequality for heat equations defined respectively on a bounded domain of $\R^d$ and the whole space $\R^d$, 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 S. Huang and M. Wang.
专家简介：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；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。
邀请人：张旭
