On the exactly synchronizable state to a coupled system of wave equations

In this paper, we discuss the determination of the exactly synchronizable state to a coupled system of wave equations. In a special case, the exactly synchronizable state can be uniquely determined whatever the boundary controls would be chosen. In the general case, the determination of the exactly synchronizable state depends on the boundary controls which realize the exact synchronization, however, we can give an estimate to the difference between the exactly synchronizable state and the solution to a problem independent of boundary controls.