Approximate Boundary Null Controllability and Approximate Boundary Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls
In this paper, for a coupled system of wave equations with Neumann boundary controls, the approximate boundary null controllability, the approximate boundary synchronization and the approximate boundary synchronization by groups are taken into account, respectively. Like in the case with Dirichlet boundary controls, the corresponding conditions of compatibility, and the criteria of Kalman’s type as necessary conditions are obtained. The sufficiency of Kalman’s criteria is further discussed in one dimensional space.
Projet supported by the National Basic Research Program of China (No 2013CB834100), and the National Natural Science Foundation of China (No 11121101).
- 2.Gohberg, I.C., Krein, M.G.: Introduction to the Theory of Linear Nonselfadjoint Operators. American Mathematical Society, Providence, RI (1969)Google Scholar
- 3.Komornik, V., Loreti, P.: Fourier Series in Control Theory. Springer Monographs in Mathematics. Springer, Berlin (2005)Google Scholar