Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Asymptotic property of a reparable multi-state device

Authors: Houbao Xu, Jingyuan Yu and Guangtian Zhu
Journal: Quart. Appl. Math. 63 (2005), 779-789
MSC (1991): Primary 93D20, 90B25; Secondary 34D05
Published electronically: October 18, 2005
MathSciNet review: 2187931
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Abstract: This paper is devoted to studying the existence, uniqueness and asymptotic stability of a multi-state device's time-dependent solution. $ C_0$ semigroup theory is used to prove the existence of a unique non-negative solution of the device. Moveover, by analyzing the spectrum of the system operator generated by the device, this paper proves that 0 is the unique spectral point on the imaginary axis and the other spectra lie in the left half plane. As a result, the asymptotic behavior of a multi-state device is obtained.

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Additional Information

Houbao Xu
Affiliation: Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
Address at time of publication: Room 709, Institute 710, No. 16 FuCheng Road, Beijing 100037, China
Email: xuhoubao@yahoo.com.cn

Jingyuan Yu
Affiliation: Beijing Institute of Information and Control, Beijing 100037, China
Email: yujy@nasic.spacechina.com

Guangtian Zhu
Affiliation: Academy of Mathematic and System Sciences, C.A.S., Beijing 100080, China

DOI: https://doi.org/10.1090/S0033-569X-05-00986-0
Keywords: Multi-state device, asymptotic stability, $C_0$-semigroup
Received by editor(s): April 17, 2005
Received by editor(s) in revised form: May 17, 2005
Published electronically: October 18, 2005
Article copyright: © Copyright 2005 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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