A RIGIDITY RESULT FOR THE HOLM-STALEY b-FAMILY OF EQUATIONS WITH APPLICATION TO THE ASYMPTOTIC STABILITY OF THE DEGASPERIS-PROCESI PEAKON

Abstract : We prove that the peakons are asymptotically H 1-stable, under the flow of the Degasperis-Procesi equation, in the class of functions with a momentum density that belongs to M + (R). The key argument is a rigidity result for uniformly in time exponentially decaying global solutions that is shared by the Holm-Staley b-family of equations for b ≥ 1. This extends previous results obtained for the Camassa-Holm equation (b = 2).
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01885442
Contributeur : Luc Molinet <>
Soumis le : lundi 1 octobre 2018 - 21:57:52
Dernière modification le : mercredi 3 octobre 2018 - 01:15:47

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  • HAL Id : hal-01885442, version 1
  • ARXIV : 1810.01775

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Luc Molinet. A RIGIDITY RESULT FOR THE HOLM-STALEY b-FAMILY OF EQUATIONS WITH APPLICATION TO THE ASYMPTOTIC STABILITY OF THE DEGASPERIS-PROCESI PEAKON. 2018. 〈hal-01885442〉

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