An observability for parabolic equations from a measurable set in time

Details An observability for parabolic equations from a measurable set in time An observability for parabolic equations from a measurable set in time

2011-09-18

arxiv.org/abs/1109.3863v1

Mathematics

Analysis of PDEs

Scientific paper

This paper presents a new observability estimate for parabolic equations in $\Omega\times(0,T)$, 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 $(0,T)$. 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.

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