Stabilization of a Boussinesq system of KdV-KdV type

A family of Boussinesq systems has recently been proposed by J. L. Bona, M. Chen, and J.-C. Saut in [2] 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-parameters family of feedback laws for which the solutions issuing from small data are globally defined and exponentially decreasing in the energy space.

• Type: Journal
• Year: 2008
• Where: SCL
• Authors: Ademir F. Pazoto, Lionel Rosier
• Keywords: Amplitude Gravity Waves, Boussinesq Systems, SCL 2008, Two-way Propagation