Stabilization of a Boussinesq system of KdV-KdV type

Ademir F. Pazoto (1) , Lionel Rosier (2)

1 IM / UFRJ - Instituto de Matemática da Universidade Federal do Rio de Janeiro
2 IECN - Institut Élie Cartan de Nancy

A family of Boussinesq systems has recently been proposed by Bona, Chen, and Saut in [J.L. Bona, M. Chen, J.-C. Saut, Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I. Derivation and linear theory, J. Nonlinear Sci. 12 (4) (2002) 283-318] to describe the two-way propagation of small-amplitude gravity waves on the surface of water in a canal. In this paper, we investigate the boundary stabilization of the Boussinesq system of KdV-KdV type posed on a bounded domain. We design a two-parameter family of feedback laws for which the solutions issuing from small data are globally defined and exponentially decreasing in the energy space.

Mots clés: Boussinesq system; Boundary control; Stabilization; Exponential stability

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Ademir F. Pazoto, Lionel Rosier. Stabilization of a Boussinesq system of KdV-KdV type. Systems and Control Letters, 2008, 57 (8), pp.595-601. ⟨10.1016/j.sysconle.2007.12.009⟩. ⟨hal-00600987⟩