本文运用线性算子半群理论研究修理工可单重休假的带有一个冷贮备部件的Gaver并联可修系统的适定性问题.文中假定部件的工作时间服从指数分布,修理时间和修理工的休假时间均服从一般连续分布.通过对描述该系统行为的偏微分方程组的规范化,并引入系统的状态空间,主算子及其定义域,我们将该系统方程转化成Banach空间中的抽象的Cauchy问题.然后,运用泛函分析中的Hille-Yosida定理、Phillips定理与Fattorini定理,我们证明了该系统存在唯一的、满足概率性质的正时间依赖解.%We study the well-posedness of the Gaver's parallel system sustained by a cold standby unit and attended by a repairman with a single vacation by utilizing the linear operator semigroup theory. It is assumed that the operating times of the units satisfy exponential distributions, the repair times and the vacation time of the repairman satisfy general continuous distributions. By normalizing the system described by differential equations, we convert the system equations into an abstract Cauchy problem in the Banach space through introducing a state space, main operators and their domains. With the help of the Hille-Yosida theorem, Phillips theorem and Fattorini theorem in functional analysis, we prove that the parallel system has a unique and positive time-dependent solution which satisfies probability condition.
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