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Asymptotic property of a reparable multi-state device
Author(s):
Houbao
Xu;
Jingyuan
Yu;
Guangtian
Zhu
Journal:
Quart. Appl. Math.
63
(2005),
779-789.
MSC (1991):
Primary 93D20, 90B25;
Secondary 34D05
Posted:
October 18, 2005
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Additional information
Abstract:
This paper is devoted to studying the existence, uniqueness and asymptotic stability of a multi-state device's time-dependent solution.  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
PII:
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
Posted:
October 18, 2005
Copyright of article:
Copyright
2005,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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