Long-Time Asymptotic Behavior of Dissipative Boussinesq System

Min Chen (1) , Olivier Goubet (2)

1 Department of Mathematics
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

In this paper, we study various dissipative mechanics associated with the Boussinesq systems which model two-dimensional small amplitude long wavelength water waves. We will show that the decay rate for the damped one-directional model equations, such as the KdV and BBM equations, holds for some of the damped Boussinesq systems which model two-directional waves.

Mots clés: water waves; two-way propagation; Boussinesq systems; dissipation; long-time asymptotics

Domaines: Equations aux dérivées partielles [math.AP]

Min Chen, Olivier Goubet. Long-Time Asymptotic Behavior of Dissipative Boussinesq System. 2006. ⟨hal-00087896⟩