Rapid Stabilization for a Korteweg-de Vries Equation From the Left Dirichlet Boundary Condition

This paper deals with the stabilization problem for the Korteweg-de Vries equation posed on a bounded interval. The control acts on the left Dirichlet boundary condition. At the right end-point, Dirichlet and Neumann homogeneous boundary conditions are considered. The proposed feedback law forces the exponential decay of the system under a smallness condition on the initial data. Moreover, the decay rate can be tuned to be as large as desired. The feedback control law is designed by using the backstepping method.