Exact boundary controllability for non-autonomous quasilinear wave equations

In this paper, we first show that quite different from the autonomous case, the exact boundary controllability for non-autonomous wave equations possesses various possibilities. Then we adopt a constructive method to establish the exact boundary controllability for one -dimensional non-autonomous quasilinear wave equations with various types of boundary conditions. Finally, we apply the results to multi-dimensional quasilinear wave equation with rotation invariance.