Stabilization of a Boussinesq system of KdV–KdV type
Pazoto_AdemirF.pdf (437.9Kb)Abstract
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.
Patrocinador
This work was achieved while the second author was
visiting the Universidade Federal do Rio de Janeiro and the Centro de Modelamiento Matematico at the Universidad de
Chile (UMI CNRS 2807). The second author thank these
institutions for their hospitality. The first author was supported
by grant 49.0987/2005-2 of the Cooperation CNPq/CONICYT
(Brasil–Chile).
Quote Item
Systems & Control Letters, Volume 57, Issue 8, Pages 595-601, 2008.
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