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 . We present also results on the well-posedness of the closed-loop systems for general time-varying feedback laws.
Citation
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." Anal. PDE 10 (5) 1089 - 1122, 2017. https://doi.org/10.2140/apde.2017.10.1089
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