Analysis & PDE

  • Anal. PDE
  • Volume 10, Number 5 (2017), 1089-1122.

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

Jean-Michel Coron, Ivonne Rivas, and Shengquan Xiang

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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.

Article information

Source
Anal. PDE, Volume 10, Number 5 (2017), 1089-1122.

Dates
Received: 2 May 2016
Revised: 29 September 2016
Accepted: 7 March 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843494

Digital Object Identifier
doi:10.2140/apde.2017.10.1089

Mathematical Reviews number (MathSciNet)
MR3668585

Zentralblatt MATH identifier
1365.93391

Subjects
Primary: 93D15: Stabilization of systems by feedback 93D20: Asymptotic stability 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Keywords
Korteweg–de Vries time-varying feedback laws stabilization controllability

Citation

Coron, Jean-Michel; Rivas, Ivonne; Xiang, Shengquan. Local exponential stabilization for a class of Korteweg–de Vries equations by means of time-varying feedback laws. Anal. PDE 10 (2017), no. 5, 1089--1122. doi:10.2140/apde.2017.10.1089. https://projecteuclid.org/euclid.apde/1510843494


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