一类时变预警可休假系统解的存在惟一性分析  

The Unique Existence of the Solution of a Time-varying Repairable System with Warning Device and Repairman Vacation

作　　者：张毛毛[1] 郭丽娜[1] 

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《数学的实践与认识》2016年第2期121-126,共6页Mathematics in Practice and Theory

基　　金：数学天元青年基金(11226249);山西省青年基础研究计划项目(2012021015-5)

摘　　要：研究了一类修理工可多重延误休假且带预警装置的简单可修复系统,其中系统的失效率和修理工的延误休假率均与系统的运行时间有关.首先运用概率分析的方法将系统模型表示为一组积-微分方程,然后将系统方程转化为一个Banach空间中的抽象半线性发展方程的初值问题,并利用C_0半群理论讨论了系统解的存在惟一性条件.In this paper, a new kind of simple repairable system with repairman vacation and warning device is discussed, in which the failure rate functions of the unit and the de- layed vacation rate function of the repairman are related to the working time of the system. The system model of a group of integro-differential equations is established by using prob- ability analysis method, which then is translated into a initial value problem of a class of abstract semi-linear evolution equation in a suitable Banach space for further study. Then the conditions Of the existence and uniqueness of the system solution are analyzed by using C0-semigroup theory.

关 键 词：多重延误休假 预警装置 半线性发展系统 C0半群理论 解的存在惟一性 

分 类 号：O226[理学—运筹学与控制论]