Semigroup Method for a System Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Finite Capacity
Semigroup Method for a System Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Finite Capacity
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由可靠机器、不可靠机器和有限容量存储缓冲器组成的系统的半群方法
DOI：
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发表时间：
2015-07
影响因子：
0.2
通讯作者：
Abdukerim Haji
中科院分区：
文献类型：
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作者：
Abdukerim Haji
研究了由可靠机器、不可靠机器和具有有限容量的存储缓冲区组成的系统。该系统可以用一组具有积分边界条件的偏微分方程来描述。利用泛函分析中的C0半群理论，证明了该系统的适定性和唯一正动力学解的存在性。然后通过分析系统算子的谱分布和由系统算子生成的半群的不可约性，证明了动态解强收敛于稳态解，从而得到了动态解的渐近稳定性.
We investigate a system consisting of a reliable machine, an unreliable machine and a storage buffer with nite capacity. This system can be described by a group of partial dierential equations with integral boundary conditions. By using C0_semigroup theory of functional analysis, we prove the well-posedness and the existence of a unique positive dynamic solution of the system. And then through analyzing the spectra distribution of the system operator and irreducibility of the semigroup generated by the system operator, we deduce that the dynamic solution converges strongly to steady state solution, thus we obtain the asymptotic stability of the dynamic solution.