学术报告（汪更生 2026.5.7）

摘要: Observability is one of the core research areas in control theory. Different forms of observability inequalities not only correspond to distinct control phenomena but also possess their own mathematical significance. For evolutionary partial differential equations (PDEs), investigating the geometric characteristics of their observable sets/regions is a key component in studying the corresponding observability inequalities. However, research in this field remains far from comprehensive. 

In this talk, we first present several distinct observability inequalities within the framework of abstract evolution equations, together with their corresponding control problems. We then introduce the concepts of observable sets and regions for evolutionary PDEs, followed by a review of existing results and main research methods regarding the geometric characteristics of these sets/regions. Finally, we outline a number of open problems related to the geometric characteristics of observable (including weakly observable) sets/regions.