UNIQUENESS OF CONSERVATIVE SOLUTIONS TO THE CAMASSA-HOLM EQUATION VIA CHARACTERISTICS

被引：80

作者：

Bressan, Alberto ^{[1
]}

Chen, Geng ^{[2
]}

Zhang, Qingtian ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 01期

基金：

美国国家科学基金会;

关键词：

Camassa-Holm equation; uniqueness; singularity; large data; characterstic; WEAK SOLUTIONS;

D O I：

10.3934/dcds.2015.35.25

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper provides a direct proof the uniqueness of solutions to the Camassa-Holm equation, based on characteristics. Given a conservative solution u = u(t, x), an equation is introduced which singles out a unique characteristic curve through each initial point. By studying the evolution of the quantities u and v = 2 arctan u(x) along each characteristic, it is proved that the Cauchy problem with general initial data u(0) is an element of H-1(R) has a unique solution, globally in time.

引用

页码：25 / 42

页数：18

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