一类带有断接部件影响的两部件可修复系统的适定性

Well-Posedness of a Two-unit Repairable System with Connecting and Disconnecting Effect

研究了一类带有断接部件影响的两相同部件串联可修系统的适定性问题。将系统方程组等价地写成一个Banach空间中的抽象Cauchy问题,利用Banach空间上的线性算子半群理论及Banach格上的正线性算子半群理论,证明了该系统的适定性及动态正解的存在性,同时,还证明了系统具有正保守性质。

In this paper,the well-posedness of a repairable system with connecting and disconnecting effect,which consists of two same units connected in series,was studied.First,the system equations could be rewritten into an abstract Cauchy problem on Banach space equivalently.Then by the semigroup theory of linear operators on Banach space and the semigroup theory of positive linear operators on Banach lattices,the well-posedness,the existence of dynamic positive solution,and the conservative property of the system were proved.