Non-uniqueness for the ab-family of equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:493

Article

Holmes, John¹  Puri, Rajan¹ 

[1] Wake Forest Univ, Dept Math & Stat, Winston Salem, NC 27109 USA

关键词: Well-posedness;    Initial value problem;    Cauchy problem;    Sobolev spaces;    Camassa-Holm equation;    Peakons;   

DOI  :  10.1016/j.jmaa.2020.124563

来源: Elsevier

【 摘 要 】

We study the cubic ab-family of equations, which includes both the Fokas-Olver-Rosenau-Qiao (FORQ) and the Novikov (NE) equations. For a not equal 0, it is proved that there exist initial data in the Sobolev space H-s, s < 3/2, with nonunique solutions. Multiple solutions are constructed by studying the collision of 2-peakon solutions. Furthermore, we prove the novel phenomenon that for some members of the family, collision between 2-peakons can occur even if the faster peakon is in front of the slower peakon. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free