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arXiv · 1810.10849

Asymptotic observability identity for the heat equation in R^d

Gengsheng Wang·Ming Wang·Yubiao Zhang
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Abstract

We build up an asymptotic observability identity for the heat equation in the whole space. It says that one can approximately recover a solution, through observing it over some countable lattice points in the space and at one time. This asymptotic identity is a natural extension of the well-known Shannon-Whittaker sampling theorem \cite{Shannon,Whittaker}. According to it, we obtain a kind of feedback null approximate controllability for impulsively controlled heat equations. We also obtain a weak asymptotic observability identity with finitely many observation lattice points. This identity holds only for some solutions to the heat equation.

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Gengsheng Wang, Ming Wang, Yubiao Zhang. 2018-10-25. Asymptotic observability identity for the heat equation in R^d. https://arxiv.org/abs/1810.10849

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