  This work is devoted to prove the exponential decay for the energy of
solutions of a higher order Korteweg -de Vries (KdV)--Benjamin-Bona-Mahony
(BBM) equation on a periodic domain with a localized damping mechanism.
Following the method in [11], which combines energy estimates, multipliers and
compactness arguments, the problem is reduced to prove the Unique Continuation
Property (UCP) for weak solutions of the model. Then, this is done by deriving
Carleman estimates for a system of coupled elliptic-hyperbolic equations.
