冷贮备可修复系统解的指数渐近稳定性  

Exponential asymptotic stability of the solution of a cold standby repairable system

作　　者：胡晓晓[1] 谢观湧 

机构地区：[1]温州医学院信息与工程学院,浙江温州325035

出　　处：《浙江师范大学学报（自然科学版）》2012年第3期258-263,共6页Journal of Zhejiang Normal University:Natural Sciences

摘　　要：讨论了具有两同型部件的冷贮备可修复系统,首先证明系统算子可以生成正压缩C0半群T(t);接着证明了T(t)是拟紧算子,且0是对应系统的主算子及其共轭算子的几何重数与代数重数为1的特征值.由此推出:该系统的时间依赖解,当时间趋向于无穷时,以指数形式收敛于系统的稳态解.It was discussed a cold standby repairable described by a group of partial equations with integral system with two identical components. The system were boundary conditions. Firstly, it was showed that the operator corresponding to the system generated a positive contraction C0-semigroup T（ t ）, and proved that T{ t ） was a quasi-compact operator. Secondly, it was verified that 0 was an eigenvalue of this operator and its adjoint operator with geometric and algebraic multiplicity one. Lastly, by using the above results, the time- dependent solution of the system strongly converged to the steady-state solution was established.

关 键 词：冷贮备可修复系统 C0半群 拟紧算子 共轭算子 

分 类 号：O177.1[理学—数学]