论文部分内容阅读
讨论了具有热储备和两个独立相同部件的平行系统在由常规错误引起失效下的渐进稳定性.首先,利用B anach空间的V o lttera算子方程得到了非负动态解的存在唯一性;然后,利用强连续线性算子半群理论证明了系统正的动态解的存在唯一性,而由于初始值不在定义域内,故得到的是m ild解.但在t>0时系统古典解存在唯一,所以此时m ild解即为古典解.最后,利用线性算子半群稳定性的结果,证明了该动态解在范数意义下收敛到稳态解,进而得到了系统的渐进稳定性.
We discuss the asymptotic stability of a parallel system with a thermal reserve and two independent identical components under failure caused by conventional errors.Firstly, the existence and uniqueness of nonnegative dynamic solutions are obtained by using V o lttera operator equations in B anach space. Then, the existence and uniqueness of the positive dynamic solution of the system are proved by the strong continuous semigroup theory of semigroups, and the m ild solution is obtained because the initial value is not within the domain of definition. However, there exists a unique classical solution to the system at t> 0 , So m ild solution is classical solution.Finally, using the result of the semigroup stability of linear operator, it is proved that the dynamic solution converges to the steady-state solution in the norm meaning, and then the asymptotic stability of the system is obtained.