Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Mathematical Physics Pub Date : 2022-12-19 DOI:10.1155/2022/6955014
Ying Zhang, Congming Peng
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Abstract

In this paper, a family of the weakly dissipative periodic Camassa-Holm type equation cubic and quartic nonlinearities is considered. The precise blow-up scenarios of strong solutions and several conditions on the initial data to guarantee blow-up of the induced solutions are described in detail. Finally, we establish a sufficient condition for global solutions.
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弱耗散广义周期Camassa-Holm方程的破波和整体存在性
本文研究了一类弱耗散周期Camassa-Holm型方程的三次和四次非线性。详细描述了强解的精确爆破场景以及初始数据上保证诱导解爆破的几个条件。最后,我们建立了全局解的一个充分条件。
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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