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We study the exponential stabilization problem for a nonlinear Korteweg-deVries equa- tion on bounded interval in cases where the linearized controlsystem is not controllable. The system has Dirichlet boundary conditions at theend-points of the interval, a Neumann nonhomogeneous boundary condition at theright end-point which is the control. We build a class of time-varying feedbacklaws for which the solutions of the closed-loop systems with small initial datadecay exponentially to 0. We present also results on the well-posedness of theclosed-loop systems for general time-varying feedback laws.

Local exponential stabilization for a class of Korteweg-de Vries equations by means of time-varying feedback laws