一类可靠性模型时间依赖解的渐近性质

摘要

研究了带无穷多个部件的,由一个可靠机器,一个不可靠机器与一个缓冲库构成的系统解的渐近性质.先讨论了对应于该系统的主算子的谱特征并且得到了在虚轴上除了0点外其它所有点都属于该主算子的豫解集,0是该主算子及其共轭算子几何重数为1的特征值.然后将该结果与作者以前的结果结合起来推出该系统的时间依赖解当时刻趋向于无穷时趋向于该系统的稳态解.%Asymptotic property of the solution of the system which consists of a reliable machine,an unreliable machine and a storage buffer with infinite many workpieces has been studied. First we consider the spectral properties of the operator corresponding to this system and obtain that all points on the imaginary axis except for zero belong to resolvent set of the operator, zero is an eigenvalue of the operator and its adjoint operator with geometric multiplicity one. Then by combining those results with our previous results we deduce that the time-dependent solution of this system converges strongly to the steady-state solution of this system.