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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (2): 282-292.doi: 10.3969/j.issn.1005-3085.2021.02.011

• • 上一篇    下一篇

一个新的推广两分量Camassa-Holm系统的持久性（英）

于浩洋1,2,   种鸽子1,2   

  1. 1- 西北大学数学学院，西安  710127
    2- 西北大学非线性研究中心，西安  710069
  • 收稿日期:2018-12-11 接受日期:2019-04-15 出版日期:2021-04-15 发布日期:2022-11-08
  • 基金资助:
    国家自然科学基金 (11471259; 11631007).

Persistence Properties for a New Generalized Two-component Camassa-Holm-type System

YU Hao-yang1,2,   CHONG Ge-zi1,2   

  1. 1- School of Mathematics, Northwest University, Xi'an 710127

    2- Center for Nonlinear Studies, Northwest University, Xi'an 710069
  • Received:2018-12-11 Accepted:2019-04-15 Online:2021-04-15 Published:2022-11-08
  • Supported by:
    The National Natural Science Foundation of China (11471259; 11631007).

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摘要： 解的长时间行为是偏微分方程研究中的一个重要问题．在很大程度上，解的性质取决于初值的性质．持久性指当初值满足无穷远处衰减的条件，则方程的解在无穷远处也衰减．在本文中，我们利用权函数估计的方法研究了一个新的推广两分量 Camassa-Holm系统初值问题解的持久性，进而给出了最优衰减估计．

关键词: 推广的Camassa-Holm系统, 最优衰减估计, 持久性

Abstract: The long time behavior of solutions is one of important problems in the study of partial differential equations. To a great degree, the properties of solutions will depend on those of initial values. The persistence properties imply that the solutions of the equations decay at infinity when the initial data satisfies the condition of decaying at infinity. In this paper, we consider the persistence properties of solutions to the initial value problem for a new generalized two-component Camassa-Holm-type system by using weight functions. Furthermore, we give an optimal decaying estimate.

Key words: generalized Camassa-Holm-type system, optimal decaying estimate, persistence properties

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