A rigidity result for the Holm-Staley b-family of equations with application to the asymptotic stability of the Degasperis-Procesi peakon - Archive ouverte HAL Access content directly
Journal Articles Nonlinear Analysis: Real World Applications Year : 2019

A rigidity result for the Holm-Staley b-family of equations with application to the asymptotic stability of the Degasperis-Procesi peakon

Luc Molinet

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).
Fichier principal
Vignette du fichier
AsymptoticStablityDP1.pdf (331.46 Ko) Télécharger le fichier
Loading...

Dates and versions

hal-01885442 , version 1 (01-10-2018)

Identifiers

Cite

Luc Molinet. A rigidity result for the Holm-Staley b-family of equations with application to the asymptotic stability of the Degasperis-Procesi peakon. Nonlinear Analysis: Real World Applications, 2019, 50, pp.675-705. ⟨hal-01885442⟩
56 View
71 Download

Altmetric

Share

Gmail Facebook X LinkedIn More