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Journal of Systems Science and Complexity

, Volume 22, Issue 4, pp 647–682 | Cite as

Control and stabilization of the Korteweg-de Vries equation: recent progresses

  • Lionel RosierEmail author
  • Bing-Yu Zhang
Article

Abstract

The study of the control and stabilization of the KdV equation began with the work of Russell and Zhang in late 1980s. Both exact control and stabilization problems have been intensively studied since then and significant progresses have been made due to many people's hard work and contributions. In this article, the authors intend to give an overall review of the results obtained so far in the study but with an emphasis on its recent progresses. A list of open problems is also provided for further investigation.

Key words

Exact controllability Korteweg-de Vries equation smoothing property stabilizability unique continuation 

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Copyright information

© Academy of Mathematics & Systems Science, Beijing, China 2009

Authors and Affiliations

  1. 1.Institut Élie Cartan, UMR 7502 UHP/CNRS/INRIAVandøeuvre-lès-Nancy CedexFrance
  2. 2.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA

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