单向关闭三部件串并联可修系统动态解的研究  

Study on dynamic solution of series-parallel repairable system with one-way closure

作　　者：李延玲 LI Yan-ling(School of Mathematics and Statistics,Qinghai Nationalities University,Xining 810007,China)

机构地区：[1]青海民族大学数学与统计学院,西宁810007

出　　处：《哈尔滨商业大学学报（自然科学版）》2018年第5期601-605,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：青海省自然科学基金项目(2018-ZJ-717)

摘　　要：讨论单向关闭三部件串并联可修系统的动态解,将系统的数学模型改写为在Banach空间中的抽象Cauchy问题,研究系统相应算子的谱特征,证明0是系统相应算子的特征值而且在虚轴上除了0以外无其他谱点,运用C_0半群理论及算子理论证明系统的适定性和非负动态解的存在唯一性.In this paper, the dynamic solution of unidirectional closed three component series repairable system was studied. The system model was rewritten into an abstract Cauchy problem in Banach space, the spectral characteristics of corresponding operators of the system was discussed, and it was proved that 0 was the eigenvalue of the corresponding operators of the system and there were no other spectral points except 0 on the virtual axis. Finally, the well-posedness and the existence of the unique positive dynamic solution of the system were proved by using C 0 semigroup theory of linear operators in the functional analysis.

关 键 词：C0半群 Dirichlet算子 动态解 适定性 

分 类 号：O213[理学—概率论与数理统计]