Local exponential stabilization for a class of Korteweg-de Vries equations by means of time-varying feedback laws - Archive ouverte HAL Access content directly
Journal Articles Analysis & PDE Year : 2017

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

Abstract

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.
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Dates and versions

hal-01467008 , version 1 (13-02-2017)
hal-01467008 , version 2 (05-03-2018)

Identifiers

  • HAL Id : hal-01467008 , version 2

Cite

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⟩
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