两同型部件温贮备可修系统解的指数渐近稳定性

运用强连续半群理论研究两同型部件温贮备可修系统解的指数渐近性质,首先证明系统所生成的C0半群T(t)是拟紧的.其次证明0是对应于系统的主算子及其共轭算子的几何重数和代数重数为1的特征值,推出在右半平面和虚轴上除0以外其他所有点都属于该算子的豫解集,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.

Exponential Asymptotic Property of the Solution of the Repairable system with Warm Standby with Two Same Parts

We study exponential asymptotic property of the Solution of the Repairable system with warm standby with Two Same Parts by using C0 semigroup theory,This system can be described by a group of partial differential equations with integral boudary condtions.First we show that the operator corresponding to these equations generates a postive contraction C0 semigroup T(t),and prove that T(t) is a quasi-compact operator.Secondly we prove that 0 is an eigenvalue of the operator and its adjoin operator with geometric multiplicity andalgebraic multiplicity one.Then conclude that all points in the right half plane and on the imaginary axis except for zero belong to the resolvent set of the operator.By using the above results we obtain that the time-dependent solution of the model strongly converges to the steady-state solution of the model.