ASYMPTOTIC STABILITY FOR SOME NON POSITIVE PERTURBATIONS OF THE CAMASSA-HOLM PEAKON WITH APPLICATION TO THE ANTIPEAKON-PEAKON PROFILE

Abstract : We continue our investigation on the asymptotic stability of the peakon. In a first step we extend our asymptotic stability result [29] in the class of functions whose negative part of the momentum density is supported in ] − ∞, x 0 ] and the positive part in [x 0 , +∞[ for some x 0 ∈ R. In a second step this enables us to prove the asymptotic stability of well-ordered train of antipeakons-peakons and, in particular, of the antipeakon-peakon profile. Finally, in the appendix we prove that in the case of a non negative momentum density the energy at the left of any given point decays to zero as time goes to +∞,. This leads to an improvement of the asymptotic stability result stated in [29].
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Pré-publication, Document de travail
In this second version, we improve the result in the appendix by proving that for a solution with.. 2018
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https://hal.archives-ouvertes.fr/hal-01768579
Contributeur : Luc Molinet <>
Soumis le : mardi 3 juillet 2018 - 09:20:01
Dernière modification le : mercredi 4 juillet 2018 - 01:16:55

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AsymptStability03:07:18.pdf
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  • HAL Id : hal-01768579, version 2
  • ARXIV : 1804.06230

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Luc Molinet. ASYMPTOTIC STABILITY FOR SOME NON POSITIVE PERTURBATIONS OF THE CAMASSA-HOLM PEAKON WITH APPLICATION TO THE ANTIPEAKON-PEAKON PROFILE. In this second version, we improve the result in the appendix by proving that for a solution with.. 2018. 〈hal-01768579v2〉

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