The Null Controllability of Transmission Wave-Schrödinger System with a Boundary Control

Ya Ping Guo; Jun Min Wang; Jing Wang; Dong Xia Zhao

doi:10.1007/s10883-024-09693-1

The Null Controllability of Transmission Wave-Schrödinger System with a Boundary Control

Ya Ping Guo^*, Jun Min Wang, Jing Wang, Dong Xia Zhao

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is devoted to investigate the null controllability of the transmission wave-Schrödinger system with only one boundary control. The domain of the system consists of two bounded intervals, where the wave and Schrödinger equations evolve, respectively. Two kinds of transmission conditions are considered: one is the simple continuous transmission, and by using the HUM method, the null controllability of the system is derived in the Hilbert space when a boundary control is added only on the wave equation. The other case is that the Schrödinger state is associated with the velocity of the wave, and we establish the null controllability of the system. It is found that the second space has more regularity.

Original language	English
Article number	27
Journal	Journal of Dynamical and Control Systems
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/s10883-024-09693-1
Publication status	Published - Sept 2024

Keywords

Boundary control
Null controllability
Transmission system

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10.1007/s10883-024-09693-1

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title = "The Null Controllability of Transmission Wave-Schr{\"o}dinger System with a Boundary Control",

abstract = "This paper is devoted to investigate the null controllability of the transmission wave-Schr{\"o}dinger system with only one boundary control. The domain of the system consists of two bounded intervals, where the wave and Schr{\"o}dinger equations evolve, respectively. Two kinds of transmission conditions are considered: one is the simple continuous transmission, and by using the HUM method, the null controllability of the system is derived in the Hilbert space when a boundary control is added only on the wave equation. The other case is that the Schr{\"o}dinger state is associated with the velocity of the wave, and we establish the null controllability of the system. It is found that the second space has more regularity.",

keywords = "Boundary control, Null controllability, Transmission system",

author = "Guo, \{Ya Ping\} and Wang, \{Jun Min\} and Jing Wang and Zhao, \{Dong Xia\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.",

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T1 - The Null Controllability of Transmission Wave-Schrödinger System with a Boundary Control

AU - Guo, Ya Ping

AU - Wang, Jun Min

AU - Wang, Jing

AU - Zhao, Dong Xia

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2024/9

Y1 - 2024/9

N2 - This paper is devoted to investigate the null controllability of the transmission wave-Schrödinger system with only one boundary control. The domain of the system consists of two bounded intervals, where the wave and Schrödinger equations evolve, respectively. Two kinds of transmission conditions are considered: one is the simple continuous transmission, and by using the HUM method, the null controllability of the system is derived in the Hilbert space when a boundary control is added only on the wave equation. The other case is that the Schrödinger state is associated with the velocity of the wave, and we establish the null controllability of the system. It is found that the second space has more regularity.

AB - This paper is devoted to investigate the null controllability of the transmission wave-Schrödinger system with only one boundary control. The domain of the system consists of two bounded intervals, where the wave and Schrödinger equations evolve, respectively. Two kinds of transmission conditions are considered: one is the simple continuous transmission, and by using the HUM method, the null controllability of the system is derived in the Hilbert space when a boundary control is added only on the wave equation. The other case is that the Schrödinger state is associated with the velocity of the wave, and we establish the null controllability of the system. It is found that the second space has more regularity.

KW - Boundary control

KW - Null controllability

KW - Transmission system

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SN - 1079-2724

VL - 30

JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

IS - 3

M1 - 27

ER -

The Null Controllability of Transmission Wave-Schrödinger System with a Boundary Control

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