冷备状态下两个相同部件并联的可修系统的进一步研究

Further Research of the Cold Standby Parallel System Consisting of Two Repairable Units

首先当μ(x)满足0<■≤μ(x)≤■<∞时证明该系统主算子生成的C0-半群是拟紧算子,然后此结果与已有的结果结合后推出该系统的解是指数稳定的,最后当μ(x)=μ时研究该主算子的所有特征值.

First we prove that the Co-semigroup generated by the operator corresponding to the repairable system consisting of two identical units is a quasi-compact operator under the assumption 0〈 ≤μ（x）≤μ^-〈∞ , then by combining the result with other known results we deduce that the time-dependent solution to the system is exponentially stable, finally we discuss all eigenvalues of the operator.