Aller au contenu  Aller au menu  Aller à la recherche

Bienvenue - Laboratoire Jacques-Louis Lions

Partenariats

CNRS

UPMC

UdP
Print this page |
5 postes ATER en mathématiques à Sorbonne Université
date limite le 5 avril à 16h
Détails ici

Chiffres-clé

Chiffres clefs

189 personnes travaillent au LJLL

90 permanents

82 chercheurs et enseignants-chercheurs permanents

8 ingénieurs, techniciens et personnels administratifs

99 personnels non permanents

73 doctorants

14 post-doc et ATER

12 émérites et collaborateurs bénévoles

 

Chiffres mars 2019

 

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.