Non-uniqueness for the Fokas-Olver-Rosenau-Qiao equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:470

Article

Himonas, A. Alexandrou¹  Holliman, Curtis² 

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] Catholic Univ Amer, Dept Math, Washington, DC 20064 USA

关键词: Fokas-Olver-Rosenau-Qiao equation;    Integrable Camassa Holm type equations;    Cauchy problem;    Well-posedness in Sobolev spaces;    Non-uniqueness and ill-posedness;    Peakon solutions;   

DOI  :  10.1016/j.jmaa.2018.10.030

来源: Elsevier

【 摘 要 】

For the Fokas-Olver-Rosenau-Qiao equation (FORQ), on both the line and the circle, it is proved that there exist initial data in the Sobolev spaces H-s, with s < 3/2, which have nonunique solutions. This phenomenon is demonstrated by constructing a 2-peakon solution with an asymmetric peakon-antipeakon initial profile. The peakon and antipeakon eventually collide, and the solution at the collision time coincides with a second solitary peakon solution. Using the time reversibility of the equation, this scenario proves nonuniqueness. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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