Energy decay rates for the coupled wave and Schrödinger system with boundary control∗

Jun Min Wang; Jing Wang

doi:10.1109/ICCA.2019.8899735

Energy decay rates for the coupled wave and Schrödinger system with boundary control^∗

Jun Min Wang, Jing Wang

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

In this paper, the boundary stabilization of an interconnected system of the Schrödinger and wave equations with boundary control is considered. By resolvent estimates together with the frequency domain method, we obtain two classes of energy decay rates:1. When the boundary control is located in the side of Schrödinger equation, the system is lack of exponential decay, but polynomial decay holds. Moreover, the optimal polynomial decay rate is further obtained for the system.2. When the boundary control is located in the side of wave equation, the system can achieve exponential stability.

Original language	English
Title of host publication	2019 IEEE 15th International Conference on Control and Automation, ICCA 2019
Publisher	IEEE Computer Society
Pages	732-737
Number of pages	6
ISBN (Electronic)	9781728111643
DOIs	https://doi.org/10.1109/ICCA.2019.8899735
Publication status	Published - Jul 2019
Event	15th IEEE International Conference on Control and Automation, ICCA 2019 - Edinburgh, United Kingdom Duration: 16 Jul 2019 → 19 Jul 2019

Publication series

Name	IEEE International Conference on Control and Automation, ICCA
Volume	2019-July
ISSN (Print)	1948-3449
ISSN (Electronic)	1948-3457

Conference

Conference	15th IEEE International Conference on Control and Automation, ICCA 2019
Country/Territory	United Kingdom
City	Edinburgh
Period	16/07/19 → 19/07/19

Access to Document

10.1109/ICCA.2019.8899735

Cite this

Wang, J. M., & Wang, J. (2019). Energy decay rates for the coupled wave and Schrödinger system with boundary control^∗. In 2019 IEEE 15th International Conference on Control and Automation, ICCA 2019 (pp. 732-737). Article 8899735 (IEEE International Conference on Control and Automation, ICCA; Vol. 2019-July). IEEE Computer Society. https://doi.org/10.1109/ICCA.2019.8899735

@inproceedings{43696394046e4947a63677ac9b2001e2,

title = "Energy decay rates for the coupled wave and Schr{\"o}dinger system with boundary control∗",

abstract = "In this paper, the boundary stabilization of an interconnected system of the Schr{\"o}dinger and wave equations with boundary control is considered. By resolvent estimates together with the frequency domain method, we obtain two classes of energy decay rates:1. When the boundary control is located in the side of Schr{\"o}dinger equation, the system is lack of exponential decay, but polynomial decay holds. Moreover, the optimal polynomial decay rate is further obtained for the system.2. When the boundary control is located in the side of wave equation, the system can achieve exponential stability.",

author = "Wang, {Jun Min} and Jing Wang",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 15th IEEE International Conference on Control and Automation, ICCA 2019 ; Conference date: 16-07-2019 Through 19-07-2019",

year = "2019",

month = jul,

doi = "10.1109/ICCA.2019.8899735",

language = "English",

series = "IEEE International Conference on Control and Automation, ICCA",

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Wang, JM & Wang, J 2019, Energy decay rates for the coupled wave and Schrödinger system with boundary control^∗. in 2019 IEEE 15th International Conference on Control and Automation, ICCA 2019., 8899735, IEEE International Conference on Control and Automation, ICCA, vol. 2019-July, IEEE Computer Society, pp. 732-737, 15th IEEE International Conference on Control and Automation, ICCA 2019, Edinburgh, United Kingdom, 16/07/19. https://doi.org/10.1109/ICCA.2019.8899735

Energy decay rates for the coupled wave and Schrödinger system with boundary control^∗. / Wang, Jun Min; Wang, Jing.
2019 IEEE 15th International Conference on Control and Automation, ICCA 2019. IEEE Computer Society, 2019. p. 732-737 8899735 (IEEE International Conference on Control and Automation, ICCA; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this paper, the boundary stabilization of an interconnected system of the Schrödinger and wave equations with boundary control is considered. By resolvent estimates together with the frequency domain method, we obtain two classes of energy decay rates:1. When the boundary control is located in the side of Schrödinger equation, the system is lack of exponential decay, but polynomial decay holds. Moreover, the optimal polynomial decay rate is further obtained for the system.2. When the boundary control is located in the side of wave equation, the system can achieve exponential stability.

AB - In this paper, the boundary stabilization of an interconnected system of the Schrödinger and wave equations with boundary control is considered. By resolvent estimates together with the frequency domain method, we obtain two classes of energy decay rates:1. When the boundary control is located in the side of Schrödinger equation, the system is lack of exponential decay, but polynomial decay holds. Moreover, the optimal polynomial decay rate is further obtained for the system.2. When the boundary control is located in the side of wave equation, the system can achieve exponential stability.

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