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arXiv · 1109.3863

An observability for parabolic equations from a measurable set in time

Kim Dang Phung·Gengsheng Wang
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Abstract

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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Kim Dang Phung, Gengsheng Wang. 2011-09-18. An observability for parabolic equations from a measurable set in time. https://arxiv.org/abs/1109.3863

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