Exact controllability of the interconnected Schrödinger and wave equations with a boundary control at the wave equation

Fei Wang; Jun Min Wang; Xiao Hui Wu

doi:10.1016/j.jmaa.2022.126831

Exact controllability of the interconnected Schrödinger and wave equations with a boundary control at the wave equation

Fei Wang^*, Jun Min Wang, Xiao Hui Wu

^*Corresponding author for this work

School of Mathematics and Statistics

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

3 Citations (Scopus)

Abstract

In this paper, we are concerned with the exact controllability of a Schrödinger equation through boundary coupling a wave equation, in which a control is designed at the wave equation. By spectral analysis, we present the asymptotic expansion for the eigenvalues and the eigenfunctions of the corresponding dual system and obtain the observability inequality. Following the duality principle, we yield the exact controllability of the coupled system.

Original language	English
Article number	126831
Journal	Journal of Mathematical Analysis and Applications
Volume	519
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2022.126831
Publication status	Published - 15 Mar 2023

Keywords

Boundary control
Exact controllability
Schrödinger equation
Wave equation

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10.1016/j.jmaa.2022.126831

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abstract = "In this paper, we are concerned with the exact controllability of a Schr{\"o}dinger equation through boundary coupling a wave equation, in which a control is designed at the wave equation. By spectral analysis, we present the asymptotic expansion for the eigenvalues and the eigenfunctions of the corresponding dual system and obtain the observability inequality. Following the duality principle, we yield the exact controllability of the coupled system.",

keywords = "Boundary control, Exact controllability, Schr{\"o}dinger equation, Wave equation",

author = "Fei Wang and Wang, {Jun Min} and Wu, {Xiao Hui}",

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AU - Wang, Fei

AU - Wang, Jun Min

AU - Wu, Xiao Hui

PY - 2023/3/15

Y1 - 2023/3/15

N2 - In this paper, we are concerned with the exact controllability of a Schrödinger equation through boundary coupling a wave equation, in which a control is designed at the wave equation. By spectral analysis, we present the asymptotic expansion for the eigenvalues and the eigenfunctions of the corresponding dual system and obtain the observability inequality. Following the duality principle, we yield the exact controllability of the coupled system.

AB - In this paper, we are concerned with the exact controllability of a Schrödinger equation through boundary coupling a wave equation, in which a control is designed at the wave equation. By spectral analysis, we present the asymptotic expansion for the eigenvalues and the eigenfunctions of the corresponding dual system and obtain the observability inequality. Following the duality principle, we yield the exact controllability of the coupled system.

KW - Boundary control

KW - Exact controllability

KW - Schrödinger equation

KW - Wave equation

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DO - 10.1016/j.jmaa.2022.126831

M3 - Article

AN - SCOPUS:85141964636

SN - 0022-247X

VL - 519

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 126831

ER -

Exact controllability of the interconnected Schrödinger and wave equations with a boundary control at the wave equation

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Keywords

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