Exact Boundary Controllability And Synchronization Of Nodal Profile For A Coupled System Of Wave Equations

Stimulated by some practical applications, the author of [26] proposed the nodal profile control. In this paper, based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, we apply a unified constructive method to establish the local exact boundary (null) controllability of nodal profile for a coupled system of1-D quasilinear wave equations with various types of boundary conditions.Furthermore, we study the synchronization of nodal profile for a coupled system of wave equations with Dirichlet type, Neumann type and third type boundary condi-tions and give examples to special cases. Based on the theory of exact boundary (null) controllability of nodal profile, we proposed a kind of system which can achieve syn-chronization of nodal profile without condition restriction on the sum of every row of coupling matrices. At last,we proposed exact boundary null controllability and syn-chronization by groups for nodal profile.