论文标题
具有耦合的罗宾边界控制的波程耦合系统的确切边界可控性和确切的边界同步
Exact boundary controllability and exact boundary synchronization for a coupled system of wave equations with coupled Robin boundary controls
论文作者
论文摘要
在本文中，我们考虑了具有耦合的罗宾边界控件的波动耦合系统的确切边界可控性和确切的边界同步（按组）。由于缺乏解决方案的难度，我们面临的挑战比Dirichlet或Neumann边界控制的情况更大。为了克服这一难度，我们使用Lasiecka和Triggiani的Neumann边界条件的混合问题解决方案的规律性结果，以使解决方案的规律性与耦合的Robin边界条件有关混合问题。因此，我们显示了系统的确切边界可控性，通过紧凑的扰动方法，我们获得了系统在某些特殊域上具有较少边界控制的系统的非外部边界可控性。基于此，我们进一步研究了同一系统的确切边界同步（按组），确定可同步状态（按组）以及耦合矩阵兼容条件的必要性。
In this paper, we consider the exact boundary controllability and the exact boundary synchronization (by groups) for a coupled system of wave equations with coupled Robin boundary controls. Owing to the difficulty coming from the lack of regularity of the solution, we confront a bigger challenge than that in the case with Dirichlet or Neumann boundary controls. In order to overcome this difficulty, we use the regularity results of solutions to the mixed problem with Neumann boundary conditions by Lasiecka and Triggiani to get the regularity of solutions to the mixed problem with coupled Robin boundary conditions. Thus we show the exact boundary controllability of the system, and by a method of compact perturbation, we obtain the non-exact boundary controllability of the system with fewer boundary controls on some special domains. Based on this, we further study the exact boundary synchronization (by groups) for the same system, the determination of the exactly synchronizable state (by groups), as well as the necessity of the compatibility conditions of the coupling matrices.
