Observability inequalities for the heat equation with bounded potentials on the whole space
Analysis of PDEs
2019-10-11 v1 Optimization and Control
Abstract
In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy localized in a subdomain, which is equidistributed over the whole space. The proof of this inequality is mainly adapted from the parabolic frequency function method, which plays an important role in proving the unique continuation property for solutions of parabolic equations. As an immediate application, we show that the null controllability holds for the heat equation with bounded potentials on the whole space.
Keywords
Cite
@article{arxiv.1910.04340,
title = {Observability inequalities for the heat equation with bounded potentials on the whole space},
author = {Yueliang Duan and Lijuan Wang and Can Zhang},
journal= {arXiv preprint arXiv:1910.04340},
year = {2019}
}
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