A higher-order BBM equation is considered with selected internal and boundary conditions as feedback laws to dissipate the energy. We propose several dissipation mechanisms leading to equations for which one has both, the global existence of solutions and non-increasing energy. Following the analysis developed in \cite{rosier} we prove that all the trajectories are attracted by the origin or the mean of initial data provided that the unique continuation property of weak solutions holds.
MSC: Primary: 35A01, 3AQ02, 35B40, 35B60, 35B65. Secondary: 35B10, 35B35