论文标题
抽象线性二阶进化系统的均匀同步
Uniform synchronization of an abstract linear second order evolution system
论文作者
论文摘要
尽管关于有限地平线的波方程同步的数学研究已经很好地发展，但长期地平线的波方程的同步几乎没有结果。本文的目的是研究在希尔伯特空间中的一个抽象线性二阶进化系统，在无限的地平线上研究均匀的同步。 首先，使用有关收缩半群的统一稳定性的经典紧凑型扰动理论，我们将建立对阻尼数量的下限，这是对所考虑系统均匀同步所必需的。然后，在最小阻尼数量下，我们阐明了系统的代数结构以及耦合矩阵兼容条件的必要性。然后，我们通过紧凑的扰动方法建立均匀的同步，然后给出渐近轨道的动力学。为具有边界反馈或（和）本地分布的反馈以及带有分布式反馈的Kirchhoff板系统提供了各种应用程序。在本文的结尾提出了一些公开问题，以供未来的发展。 该研究基于同步理论和半群的紧凑扰动。
Although the mathematical study on the synchronization of wave equations at finite horizon has been well developed, there was few results on the synchronization of wave equations for long-time horizon. The aim of the paper is to investigate the uniform synchronization at the infinite horizon for one abstract linear second order evolution system in a Hilbert space. First, using the classical compact perturbation theory on the uniform stability of semigroups of contractions, we will establish a lower bound on the number of damping, necessary for the uniform synchronization of the considered system. Then, under the minimum number of damping, we clarify the algebraic structure of the system as well as the necessity of the conditions of compatibility on the coupling matrices. We then establish the uniform synchronization by the compact perturbation method and then give the dynamics of the asymptotic orbit. Various applications are given for the system of wave equations with boundary feedback or (and) locally distributed feedback, and for the system of Kirchhoff plate with distributed feedback. Some open questions are raised at the end of the paper for future development. The study is based on the synchronization theory and the compact perturbation of semigroups.
