一类由可修,可靠的人与机器构成的系统解的渐近性质

Asymptotic Property of the Solution of the Model Describing a Repairable,Standby Human & Machine System

运用C0-半群理论研究一类由可修,可靠的人与机器构成的系统解的渐近性质.首先证明在虚轴上除了0以外其他所有点都属于该算子的豫解集,其次证明0是对应于该系统的主算子及其共轭算子的几何与代数重数为1的特征值,由此推出该系统的时间依赖解当时刻趋向于无穷时强收敛于系统的稳态解.

We study asymptotic property of the solution of the model describing a repairable, standby human machine system by using C0-semigroup theory. First we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator corresponding to the model, second prove that 0 is an eigenvalue of the operator and its adjoint operator with geometric multiplicity and algebraic multiplicity one, last by using theabove results we obtain that the time-dependent solution of the model strongly converges to the steady-state solution of the model.