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).
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Contributor : Luc Molinet <>
Submitted on : Monday, October 1, 2018 - 9:57:52 PM
Last modification on : Monday, January 13, 2020 - 2:34:44 PM
Long-term archiving on: Wednesday, January 2, 2019 - 3:23:59 PM

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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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