  Let a fourth and a second order evolution equations be coupled via the
interface by transmission conditions, and suppose that the first one is
stabilized by a localized distributed feedback. What will then be the effect of
such a partial stabilization on the decay of solutions at infinity? Is the
behavior of the first component sufficient to stabilize the second one? The
answer given in this paper is that sufficiently smooth solutions decay
logarithmically at infinity even the feedback dissipation affects an
arbitrarily small open subset of the interior. The method used, in this case,
is based on a frequency method, and this by combining a contradiction argument
with the Carleman estimates technique to carry out a special analysis for the
resolvent.
