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

Jean-Michel Coron (1) , Ivonne Rivas (1) , Shengquan Xiang (1)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equation on 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, 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.

Mots clés: Korteweg-de Vries; Time-varying feedback laws; Stabilization; Controllability

Domaines: Mathématiques [math]

Jean-Michel Coron, Ivonne Rivas, Shengquan Xiang. Local exponential stabilization for a class of Korteweg-de Vries equations by means of time-varying feedback laws. Analysis & PDE, 2017, 10 (5), pp.1089--1122. ⟨hal-01467008v2⟩