Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics
Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics
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DOI：
10.3934/dcds.2015.35.25
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发表时间：
2014-01
影响因子：
1.1
通讯作者：
A. Bressan;Geng Chen;Qingtian Zhang
中科院分区：
文献类型：
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作者：
A. Bressan;Geng Chen;Qingtian Zhang
本文利用特征线直接证明了Camassa-Holm方程解的唯一性。给定一个保守解u = u（t，x），引入一个方程，通过每个初始点选出一条唯一的特征曲线。通过研究量u和v = 2 arctanux沿着每一特征的演化，证明了具有一般初值u 0 ∈ H1（IR）的Cauchy问题在时间上全局存在唯一解.
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 = 2arctanux along each characteristic, it is proved that the Cauchy problem with general initial data u0 ∈ H 1 (IR) has a unique solution, globally in time.