#### Vol. 10, No. 5, 2017

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

### Jean-Michel Coron, Ivonne Rivas and Shengquan Xiang

Vol. 10 (2017), No. 5, 1089–1122
##### Abstract

We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equation on a bounded interval in cases where the linearized control system is not controllable. The system has Dirichlet boundary conditions at the end-points of the interval and a Neumann nonhomogeneous boundary condition at the right end-point, which is the control. We build a class of time-varying feedback laws for which the solutions of the closed-loop systems with small initial data decay exponentially to $0$. We present also results on the well-posedness of the closed-loop systems for general time-varying feedback laws.

##### Keywords
Korteweg&ndash;de Vries, time-varying feedback laws, stabilization, controllability
##### Mathematical Subject Classification 2010
Primary: 93D15, 93D20, 35Q53