  This paper is addressed to a stabilization problem of a system coupled by a
wave and a Euler-Bernoulli plate equation. Only one equation is supposed to be
damped. Under some assumption about the damping and the coupling terms, it is
shown that sufficiently smooth solutions of the system decay logarithmically at
infinity without any geometric conditions on the effective damping domain. The
proofs of these decay results rely on the interpolation inequalities for the
coupled elliptic-parabolic systems and make use of the estimate of the
resolvent operator for the coupled system. The main tools to derive the desired
interpolation inequalities are global Carleman estimates.
