Volume 29, 2023
|Number of page(s)
|31 July 2023
Controllability of the Schrödinger equation on unbounded domains without geometric control condition
FernUniversität in Hagen, Fakultät für Mathematik und Informatik, Hagen, Germany
* Corresponding author: email@example.com
Accepted: 4 May 2023
We prove controllability of the Schrödinger equation in ℝd in any time T > 0 with internal control supported on nonempty, periodic, open sets. This demonstrates in particular that controllability of the Schrödinger equation in full space holds for a strictly larger class of control supports than for the wave equation and suggests that the control theory of Schrödinger equation in full space might be closer to the diffusive nature of the heat equation than to the ballistic nature of the wave equation. Our results are based on a combination of Floquet-Bloch theory with Ingham-type estimates on lacunary Fourier series.
Mathematics Subject Classification: 93Bxx / 35Q93
Key words: Controllability / Schrödinger equation / observability estimate / Floquet-Bloch theory
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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