Asymptotic property of a reparable multi-state device

Houbao Xu; Jingyuan Yu; Guangtian Zhu

doi:10.1090/S0033-569X-05-00986-0

Asymptotic property of a reparable multi-state device

Houbao Xu^*
, Jingyuan Yu
, Guangtian Zhu

^*Corresponding author for this work

School of Mathematics and Statistics

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

20 Citations (Scopus)

Abstract

This paper is devoted to studying the existence, uniqueness and asymptotic stability of a multi-state device's time-dependent solution. C₀ 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.

Original language	English
Pages (from-to)	779-789
Number of pages	11
Journal	Quarterly of Applied Mathematics
Volume	63
Issue number	4
DOIs	https://doi.org/10.1090/S0033-569X-05-00986-0
Publication status	Published - Dec 2005

Keywords

Asymptotic stability
C-semigroup
Multi-state device

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Cite this

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N2 - This paper is devoted to studying the existence, uniqueness and asymptotic stability of a multi-state device's time-dependent solution. C0 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.

AB - This paper is devoted to studying the existence, uniqueness and asymptotic stability of a multi-state device's time-dependent solution. C0 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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KW - C-semigroup

KW - Multi-state device

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Asymptotic property of a reparable multi-state device

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Keywords

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