  In this paper, we deal with the boundary controllability and boundary
stabilizability of the 1D wave equation in non-cylindrical domain of the form
($\alpha (t)<x<\beta (t)$). By using the characteristics method, we prove under
a natural assumption on the boundary functions that the 1D wave equation is
controllable and stabilizable from one side of the boundary. Furthermore, the
control function and the decay rate of solution are given explicitly
