修理工多重延误休假的三部件并-串联退化可修复系统的适定性  

Well-posedness of a Parallel-series Repairable Deteriorating System Consisting of Three Units with Multiple Delay Vacations of Repairman

作　　者：胡倩 阿不都克热木·阿吉[1] 秦壮言 涂安然 HU Qian;ABDUKERIM Haji;QIN Zhuang-yan;TU An-ran(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学的实践与认识》2021年第9期108-136,共29页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11761066)。

摘　　要：研究了修理工多重延误休假的三部件并-串联退化可修复系统,该系统用带有边界条件和初始条件的无穷多个偏微分方程来表示.运用泛函分析中的C_(0)-半群理论来证明系统的解是存在并且唯一的.通过数值算例对系统进行了模拟,得到的结论与理论上证明的结论一致.In this paper,we study a parallel-series repairable deteriorating system consisting of three units with multiple delay vacations of repairman,which is described by infinitely many differential equations with boundary conditions and initial conditions.By using the Co-semigroup theory and operator theory,we prove the well-posedness and the existence of a unique nonnegative dynamic solutions of the system,and by using a numerical example to simulate the system,and the results obtained are consistent with those proved theoretically.

关 键 词：并-串联可修复退化系统 C0-半群理论 适定性 

分 类 号：O213.2[理学—概率论与数理统计]