报告地点：行健楼学术活动室526
邀请人：吴奕飞教授
报告人：汪更生，天津大学应用数学教授，主要研究分布参数系统控制理论尤其是偏微分方程的能控能观性、能稳性和时间最优控制等，特别的，在热方程与薛定谔方程的能观性不等式方面作出重要贡献。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。
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 H. Shanlin and M. Wang.
