  In this work, we are interested in a detailed qualitative analysis of the
Kawahara equation, a model that has numerous physical motivations such as
magneto-acoustic waves in a cold plasma and gravity waves on the surface of a
heavy liquid. First, we design a feedback control law, which combines a damping
component and another one of finite memory-type. Then, we are capable of
proving that the problem is well-posed under a condition involving the feedback
gains of the boundary control and the memory kernel. Afterwards, it is shown
that the energy associated with this system exponentially decays.
