Dispersive limit from the Kawahara to the KdV equation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Differential Equations Année : 2013

Dispersive limit from the Kawahara to the KdV equation

Yuzhao Wang
  • Fonction : Auteur
  • PersonId : 924755

Résumé

We investigate the limit behavior of the solutions to the Kawahara equation $$ u_t +u_{3x} +\varepsilon u_{5x} + u u_x =0 , $$ as $ 0<\varepsilon \to 0 $. In this equation, the terms $ u_{3x} $ and $ \varepsilon u_{5x} $ do compete together and do cancel each other at frequencies of order $ 1/\sqrt{\varepsilon} $. This prohibits the use of a standard dispersive approach for this problem. Nervertheless, by combining different dispersive approaches according to the range of spaces frequencies, we succeed in proving that the solutions to this equation converges in $ C([0,T];H^1(\R)) $ towards the solutions of the KdV equation for any fixed $ T>0$.
Fichier principal
Vignette du fichier
Kawahara-KdV_5.pdf (256.68 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00694082 , version 1 (03-05-2012)
hal-00694082 , version 2 (07-06-2012)

Identifiants

Citer

Luc Molinet, Yuzhao Wang. Dispersive limit from the Kawahara to the KdV equation. Journal of Differential Equations, 2013, 255 (8), pp.2196-2219. ⟨hal-00694082v2⟩
135 Consultations
209 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More