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Control and stabilization of the Korteweg-de Vries equation: recent progresses. (English) Zbl 1300.93091

Summary: 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.

MSC:

93C20 Control/observation systems governed by partial differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
93B05 Controllability
93D99 Stability of control systems
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