A rigidity result for the Holm–Staley b-family of equations with application to the asymptotic stability of the Degasperis–Procesi peakon. (December 2019)

• Record Type: Journal Article
• Authors: Molinet, Luc
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 675
• Page End: 705
• Publication Date: 2019-12
• Subjects: b-family of equations -- Degasperis–Procesi -- Rigidity property -- Asymptotic stability -- Peakon; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.06.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We prove that the peakons are asymptotically 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 ).