  The goal of this work is to study a model of the wave equation with dynamic
boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin
method combined with the fixed point theorem, we show the existence and
uniqueness of a local in time solution. Second, we show that under some
restrictions on the initial data, the solution continues to exist globally in
time. On the other hand, if the interior source dominates the boundary damping,
then the solution is unbounded and grows as an exponential function. In
addition, in the absence of the strong damping, then the solution ceases to
exist and blows up in finite time.
