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Journal d'Analyse Mathématique

, Volume 137, Issue 1, pp 291–337 | Cite as

Stabilization of a Boussinesq system with localized damping

  • Sorin MicuEmail author
  • Ademir F. Pazoto
Article
  • 25 Downloads

Abstract

A family of Boussinesq systems was proposed by J. L. Bona, M. Chen, and J.-C. Saut to describe the two-way propagation of small amplitude gravity waves on the surface of water in a canal. Our work considers a class of these Boussinesq systems which couples two Benjamin-Bona-Mahony type equations posed on a bounded interval. We study the stabilization of the resulting system when a localized damping term acts in one equation only. By means of spectral analysis and eigenvectors expansion of solutions, we prove that the energy associated to the model converges to zero as time tends to infinity. Also, we address the problem of unique continuation property for the corresponding conservative system.

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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CraiovaCraiovaRomania
  2. 2.Institute of Mathematical Statistics and Applied MathematicsBucharestRomania
  3. 3.Institute of MathematicsFederal University of Rio de Janeiro, UFRJRio de JaneiroBrasil

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