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Seminar on Analysis, Geometry, and PDEs


Tid: 2021-09-21 15:15 till 16:15
Plats: This talk is given on Zoom. If you wish to receive and invitation, please email the organizer.
Kontakt: eskil [dot] rydhe [at] math [dot] lu [dot] se
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Asymptotic stability of Novikov peakons

Speaker: Wei Lian / Harbin Engineering University

Abstract: In this talk, we will consider a quasilinear dispersive equation, i.e., the Novikov equation, and show the asymptotic stability of the peaked solitary waves. Such a result is based on a rigidity property of Novikov solutions with some "localized" structure. The new ideas in it could be potentially useful in studying the asymptotic stability of peaked solitary waves to a wider class of models. Following Molinet's approach for the Camassa-Holm equation, we managed to overcome the lack of conservation of momentum densities of solutions by redesigning the localization of the total mass from the finite speed of propagation property of the momentum densities and exploring the uniform in time exponential decay property of the solutions from the localization of the H1 energy.