  In this paper we study exact boundary controllability for a linear wave
equation with strong and weak interior degeneration of the coefficient in the
principle part of the elliptic operator. The objective is to provide a
well-posedness analysis of the corresponding system and derive conditions for
its controllability through boundary actions. Passing to a relaxed version of
the original problem, we discuss existence and uniqueness of solutions, and
using the HUM method we derive conditions on the rate of degeneracy for both
exact boundary controllability and the lack thereof.
