Asymptotic observability identity for the heat equation in R^d
Analysis of PDEs
2018-10-26 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1810.10849,
title = {Asymptotic observability identity for the heat equation in R^d},
author = {Gengsheng Wang and Ming Wang and Yubiao Zhang},
journal= {arXiv preprint arXiv:1810.10849},
year = {2018}
}