Well-posedness and stabilization of the Benjamin-Bona-Mahony equation on star-shaped networks

Kaïs Ammari (1) , Emmanuelle Crépeau (2, 3)

1 Département de Mathématiques [Monastir]
2 LMV - Laboratoire de Mathématiques de Versailles
3 EDP - Equations aux Dérivées Partielles

We study the stabilization issue of the Benjamin–Bona–Mahony (BBM) equation on a finite star-shaped network with a damping term acting on the central node. In a first time, we prove the well-posedness of this system. Then thanks to the frequency domain method, we get the asymptotic stabilization result.

Domaines: Optimisation et contrôle [math.OC]

Kaïs Ammari, Emmanuelle Crépeau. Well-posedness and stabilization of the Benjamin-Bona-Mahony equation on star-shaped networks. Systems and Control Letters, 2019, 127, pp.39-43. ⟨10.1016/j.sysconle.2019.03.005⟩. ⟨hal-02044249⟩