On the Benjamin-Bona-Mahony equation with a localized damping

Lionel Rosier (1)

1 CAS - Centre Automatique et Systèmes

We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedback law, or a boundary feedback law. In each case, we prove the global wellposedness of the system and the convergence towards a solution of the BBM equation which is null on a band. If the Unique Continuation Property holds for the BBM equation, this implies that the origin is asymp-totically stable for the damped BBM equation.

Mots clés: Benjamin-Bona-Mahony equation; unique continuation property; internal stabilization; boundary stabilization

Domaines: Equations aux dérivées partielles [math.AP]

Lionel Rosier. On the Benjamin-Bona-Mahony equation with a localized damping. 2016. ⟨hal-01323704⟩