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

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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.

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Authors and Affiliations

  1. Institut Élie Cartan, UMR 7502 UHP/CNRS/INRIA, B.P. 239, F-54506, Vandøeuvre-lès-Nancy Cedex, France

    Lionel Rosier

  2. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio, 45221-0025, USA

    Bing-Yu Zhang

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  1. Lionel Rosier
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  2. Bing-Yu Zhang
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Correspondence to Lionel Rosier.

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The paper is dedicated to the Institute of System Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences for its 30th anniversary.

Report of the 14th meeting of the British Association for the Advancement of Science, York, September 1844 (London 1845), pp 311{390, Plates XLVII-LVII

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Rosier, L., Zhang, BY. Control and stabilization of the Korteweg-de Vries equation: recent progresses. J Syst Sci Complex 22, 647–682 (2009). https://doi.org/10.1007/s11424-009-9194-2

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