| Autor: |
Wang, Gengsheng, Wang, Ming, Zhang, Yubiao |
| Rok vydání: |
2018 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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