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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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Vol. 10 (2017), No. 5, 1089–1122
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Abstract |
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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. |
Keywords
Korteweg–de Vries, time-varying feedback laws,
stabilization, controllability
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Mathematical Subject Classification 2010
Primary: 93D15, 93D20, 35Q53
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Milestones
Received: 2 May 2016
Revised: 29 September 2016
Accepted: 7 March 2017
Published: 1 July 2017
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Authors |
| Jean-Michel Coron | |
| Université Pierre et Marie Curie -
Paris 6 UMR 7598 Laboratoire Jacques-Louis Lions 75005 Paris France |
ETH Zürich Institute for Theoretical Studies 8092 Zürich Switzerland |
| Ivonne Rivas | |
| Universidad del Valle Departamento de Matemáticas Cali AA 25360 Colombia |
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| Shengquan Xiang | |
| Université Pierre et Marie Curie -
Paris 6 UMR 7598 Laboratoire Jacques-Louis Lions 75005 Paris France |
ETH Zürich Institute for Theoretical Studies and Forschungsinstitut für Mathematik 8092 Zürich Switzerland |
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