On the Benjamin-Bona-Mahony Equation with a Localized Damping (Journal of Mathematical Study, 2016)
We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedbacklaw, or a boundary feedback law. In each case, we prove the global well-posednessof the system and the convergence towards a solution of the BBM equation which isnull on a band. If the Unique Continuation Property holds for the BBM equation, thisimplies that the origin is asymptotically stable for the damped BBM equation.
Keywords: Benjamin-Bona-Mahony equation; unique continuation property; internal stabilization; boundary stabilization.