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Article Dans Une Revue Journal of Differential Equations Année : 2015

Asymptotic stability of a nonlinear Korteweg-de Vries equation with a critical length

Résumé

We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0,2pi). The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove that the origin is (locally) asymptotically stable for the nonlinear system.
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Dates et versions

hal-00834475 , version 1 (15-06-2013)

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Jixun Chu, Jean-Michel Coron, Peipei Shang. Asymptotic stability of a nonlinear Korteweg-de Vries equation with a critical length. Journal of Differential Equations, 2015, 259 (8), pp.4045--4085. ⟨10.1016/j.jde.2015.05.010⟩. ⟨hal-00834475⟩
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