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| HAL : hal-00694082, version 2 |
| arXiv : 1205.0729 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (03-05-2012) | v2 (07-06-2012) |
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| Dispersive limit from the Kawahara to the KdV equation |
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| Luc Molinet 1Yuzhao Wang 2 |
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| (03/05/2012) |
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| 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$. |
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| 1 : | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| 2 : | Department of Mathematics and Physics |
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North China Electric Power University |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| KdV equation – Kawahara equation – dispersive limit |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00694082, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00694082 | |
| oai:hal.archives-ouvertes.fr:hal-00694082 | |
| Contributeur : Luc Molinet | |
| Soumis le : Jeudi 7 Juin 2012, 11:27:55 | |
| Dernière modification le : Jeudi 7 Juin 2012, 14:27:14 | |
