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Stabilization of a Boussinesq system of KdV–KdV type

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2008-08
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Pazoto, Ademir F.
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Stabilization of a Boussinesq system of KdV–KdV type
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Author
  • Pazoto, Ademir F.;
  • Rosier, Lionel;
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.
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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).
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URI: https://repositorio.uchile.cl/handle/2250/125084
ISSN: 0167-6911
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Systems & Control Letters, Volume 57, Issue 8, Pages 595-601, 2008.
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