  This work is concerned with the possibility of proving the boundary null
controllability for the degenerate wave equation, developing the asymptotic
analysis of a suitable family of state-control pairs $((u_\varepsilon ,
v_\varepsilon))_{\varepsilon >0}$, solving related internal null
controllability problems. The passage to the limit argument will be rigorously
performed through the obtainment of a refined observalitity type inequality,
with a constant explicitly given in terms of $\varepsilon >0$. This represents
an essential point, since will allow us to achieve our required weak
convergence results.
