An observability estimate for parabolic equations from a measurable set in time and its applications

摘要

This paper presents a new observability estimate for parabolic equations in .0; T /, where is a convex domain. The observation region is restricted over a product set of an open nonempty subset of and a subset of positive measure in .0; T /. This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.