论文标题
非自主一级双曲线系统的有限时间稳定
Finite Time Stabilization of Nonautonomous First Order Hyperbolic Systems
论文作者
论文摘要
我们解决了非自主的初始边界价值问题的脱钩线性一维双曲系统，研究有限的时间稳定现象。我们建立了足够和必要的条件，以确保在任何初始$ l^2 $ -DATA的有限时间内解决方案稳定在零。在非自主情况下，我们给出了一个组合标准，指出且仅当反射边界系数的矩阵与有向的无环图相对应时，就会发生稳健稳定。等效的鲁棒代数标准是该图的邻接矩阵是nilpotent的。在自主情况下，我们还提供了一个光谱稳定标准，相对于双曲系统系数的扰动，这是不重做的。
We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions ensuring that solutions stabilize to zero in a finite time for any initial $L^2$-data. In the nonautonomous case we give a combinatorial criterion stating that the robust stabilization occurs if and only if the matrix of reflection boundary coefficients corresponds to a directed acyclic graph. An equivalent robust algebraic criterion is that the adjacency matrix of this graph is nilpotent. In the autonomous case we also provide a spectral stabilization criterion, which is nonrobust with respect to perturbations of the coefficients of the hyperbolic system.
