论文标题
与边界控制的流体传递管的稳定性问题相关的特征函数和特征向量的riesz基础
The Riesz basisness of the eigenfunctions and eigenvectors connected to the stability problem of a fluid-conveying tube with boundary control
论文作者
论文摘要
在本文中，我们研究了通过边界控制的拉伸管输送流体的稳定性问题。抽象光谱问题涉及表格的操作铅笔\ begin {equination*} \ Mathcal {m} \ left（λ\右）=λ^2g+λd+c \ quad \ quad \ quad \ text {and} \ quad \ quad \ quad \ quad \ quad \ mathcal {p}空间。对相应的本征函数和特征向量的复杂平面中特征值的位置和渐近分析进行了彻底的分析。 Well-posedness of the closed-loop system represented by the initial-value problem for the abstract equation \begin{equation*} \dot{x}\left(t\right)=Tx\left(t\right) \end{equation*} is established in the framework of semigroups as well as expansions of the solutions in terms of eigenvectors and stability of the closed-loop system operator $ t $。对于问题的参数，我们给出的区域比文献中的区域更大，其中文献中有一个带有流动的管，一端仅支撑，在另一端应用边界控制器，可以指数稳定。
In the present paper we study the stability problem for a stretched tube conveying fluid with boundary control. The abstract spectral problem concerns operator pencils of the forms \begin{equation*} \mathcal{M}\left(λ\right)=λ^2G+λD+C\quad\text{and}\quad\mathcal{P}\left(λ\right)=λI-T \end{equation*} taking values in different Hilbert product spaces. Thorough analysis is made of the location and asymptotics of eigenvalues in the complex plane and Riesz basisness of the corresponding eigenfunctions and eigenvectors. Well-posedness of the closed-loop system represented by the initial-value problem for the abstract equation \begin{equation*} \dot{x}\left(t\right)=Tx\left(t\right) \end{equation*} is established in the framework of semigroups as well as expansions of the solutions in terms of eigenvectors and stability of the closed-loop system operator $T$. For the parameters of the problem we give regions, larger than those in the literature, in which a stretched tube with flow, simply supported at one end, with a boundary controller applied at the other end, can be made exponentially stable.
