具有耦合Robin边界控制的wave equations耦合系统的精确边界能控性和精确边界同步
Exact boundary controllability and exact boundary synchronization for a coupled system of wave equations with coupled Robin boundary controls
摘要：
本文研究了一类具有耦合Robin边界控制的耦合波动方程组的精确边界能控性和精确边界同步性。由于解的缺乏正则性带来的困难，我们面临着比Dirichlet或Neumann边界控制更大的挑战。为了克服这一困难，我们利用Lasiecka和Triggiani关于Neumann边界条件混合问题解的正则性结果，得到了耦合Robin边界条件混合问题解的正则性.利用紧扰动方法，在某些特殊区域上，得到了具有较少边界控制的系统的非精确边界能控性.在此基础上，我们进一步研究了同一系统的精确边界同步（分组），精确可同步状态（分组）的确定，以及耦合矩阵相容条件的必要性。
英文摘要：
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.
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