Well-posedness and stability of the repairable system with N failure modes and one standby unit

doi:10.1016/j.jmaa.2010.08.063

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	Well-posedness and stability of the repairable system with N failure modes and one standby unit
	Zheng, Fu 1,2; Zhu, Guangtian 3; Gao, Chao 4
	2011-03-01
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	375 期号:1 页码:174-184
摘要	The well-posedness and stability of the repairable system with N failure modes and one standby unit were discussed by applying the c(0) semigroups theory of function analysis. Firstly, the integro-differential equations described the system were transformed into some abstract Cauchy problem of Banach space. Secondly, the system operator generates positive contractive c(0) semigroups T (t) and so the well-posedness of the system was obtained. Finally, the spectral distribution of the system operator was analyzed. It was proven that 0 is strictly dominant eigenvalue of the system operator and the dynamic solution of the system converges to the steady-state solution. The steady-state solution was shown to be the eigenvector of the system operator corresponding to the eigenvalue 0. At the same time the dynamic solution exponentially converges to the steady-state solution. (C) 2010 Elsevier Inc. All rights reserved.
关键词	Repairable system c(0) Semigroups Well-posedness Asymptotic stability Strictly dominant eigenvalue Exponential stability
DOI	10.1016/j.jmaa.2010.08.063
语种	英语
资助项目	Bohai University ; Daqing Normal University[08ZQ06]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000284293600015
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11612
专题	中国科学院数学与系统科学研究院
通讯作者	Zheng, Fu
作者单位	1.Bohai Univ, Dept Math, Jinzhou 121013, Liaoning, Peoples R China 2.Beijing Inst Informat & Control, Dept Syst Engn, Beijing 100037, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 4.Yanbian Univ, Dept Math, Yanji 133002, Peoples R China
推荐引用方式 GB/T 7714	Zheng, Fu,Zhu, Guangtian,Gao, Chao. Well-posedness and stability of the repairable system with N failure modes and one standby unit[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2011,375(1):174-184.
APA	Zheng, Fu,Zhu, Guangtian,&Gao, Chao.(2011).Well-posedness and stability of the repairable system with N failure modes and one standby unit.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,375(1),174-184.
MLA	Zheng, Fu,et al."Well-posedness and stability of the repairable system with N failure modes and one standby unit".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 375.1(2011):174-184.