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Bienvenue - Laboratoire Jacques-Louis Lions




Paris Cité
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Key figures

Key figures

189 people work at LJLL

86 permanent staff

80 researchers and permanent lecturers

6 engineers, technicians and administrative staff

103 non-permanent staff

74 Phd students

15 post-doc and ATER

14 emeritus scholars and external collaborators


January 2022


GdT Thésards : S. Tang

Asymptotic stability of a Korteweg-de Vries equation with a two-dimensional center manifold

Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg-de Vries equation posed on a finite interval (0,2π (7/3)^(1/2) ). The equation comes with a Dirichlet boundary condition at the left end-point and both of the Dirichlet and Neumann homogeneous boundary conditions at he right endpoint. It is known that the associated linearized equation around the origin is not asymptotically stable. In this paper, the nonlinear Korteweg-de Vries equation is proved to be locally asymptotically stable around the origin through the center manifold method. In particular, the existence of a two-dimensional local center manifold is presented, which is locally exponentially attractive. By analyzing the Korteweg-de Vries equation restricted on the local center manifold, a polynomial decay rate of the solution is obtained.