On conservative sticky peakons to the modified Camassa-Holm equation

被引：2

作者：

Gao, Yu ^{[1
]}

机构：

[1] Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Kowloon, Hong Kong, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 365卷

基金：

中国国家自然科学基金;

关键词：

Integrable system; Sticky particles; Conservative solutions; Non-collision regularization; Singular product; GLOBAL WEAK SOLUTIONS; SHALLOW-WATER; BLOW-UP; DISSIPATIVE SOLUTIONS; MULTIPEAKON SOLUTIONS; LAX INTEGRABILITY; CAUCHY-PROBLEM; WAVE-BREAKING; UNIQUENESS; EXISTENCE;

D O I：

10.1016/j.jde.2023.04.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use a sticky particle method to show global existence of (energy) conservative sticky N-peakon solutions to the modified Camassa-Holm equation. A dispersion regularization is provided as a selection principle for the uniqueness of conservative N-peakon solutions. The dispersion limit avoids the collision between peakons, and numerical results show that the dispersion limit is exactly the sticky peakons. At last, when the splitting of peakons is allowed, we give an example to show the non-uniqueness of conservative solutions.(c) 2023 Elsevier Inc. All rights reserved.

引用

页码：486 / 520

页数：35

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