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

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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https://hal.archives-ouvertes.fr/hal-00625082
Contributor : Kim Dang Phung <>
Submitted on : Tuesday, September 20, 2011 - 4:12:12 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM

### Citation

Kim Dang Phung, Gengsheng Wang. An observability estimate for parabolic equations from a measurable set in time and its applications. Journal of the European Mathematical Society, European Mathematical Society, 2013, 15 (2), pp. 681-703. ⟨10.4171/JEMS/371⟩. ⟨hal-00625082⟩

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