Abstract
This paper presents a new observability estimate for parabolic equations in \Omega\times\left( 0,T\right) , where \Omega is a convex domain. The observation region is restricted over a product set of an open nonempty subset of \Omega and a subset of positive measure in \left( 0,T\right) . 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.
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