  This paper is devoted to a study of the null controllability problems for
one-dimensional linear degenerate wave equations through a boundary controller.
First, the well-posedness of linear degenerate wave equations is discussed.
Then the null controllability of some degenerate wave equations is established,
when a control acts on the non-degenerate boundary. Different from the known
controllability results in the case that a control acts on the degenerate
boundary, any initial value in state space is controllable in this case. Also,
an explicit expression for the controllability time is given. Furthermore, a
counterexample on the controllability is given for some other degenerate wave
equations.
