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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 ›› 2015, Vol. 32 ›› Issue (5): 783-790.doi: 10.3969/j.issn.1005-3085.2015.05.015

• • 上一篇    

Fornberg-Whitham方程解的解析性和持久性(英)

赵彩霞1,2,   付  英1   

  1. 1- 西北大学数学学院，西安 710127
    2- 山西省忻州市实验中学，忻州 034000
  • 收稿日期:2013-06-17 接受日期:2014-06-23 出版日期:2015-10-15 发布日期:2015-12-15
  • 基金资助:
    国家自然科学基金 (11001219; 11471259); 陕西省自然科学基金 (2014JQ1002).

Analyticity and Persistence Properties of Solutions to the Fornberg-Whitham Equation

ZHAO Cai-xia1,2,   FU Ying1   

  1. 1- School of Mathematics, Northwest University, Xi'an 710127
    2- Experimental Middle School of Xinzhou of Shanxi Province, Xinzhou 034000
  • Received:2013-06-17 Accepted:2014-06-23 Online:2015-10-15 Published:2015-12-15
  • Supported by:
    The National Natural Science Foundation of China (11001219; 11471259); the Natural Science Foundation of Shaanxi Province (2014JQ1002).

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摘要： 解的长时间行为是偏微分方程研究中的重要问题之一，而初值的性质在很大程度上决定了偏微分方程解的性质．本文研究了Fornberg-Whitham方程Cauchy问题当初值解析或衰减时解的解析性和持久性．证明了解对于两个变量都是解析的，其中对空间变量全局解析，时间变量局部解析，而当初值衰减时解在后面任何时间一致衰减．

关键词: Fornberg-Whitham方程, 解析解, 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. In this paper, the analyticity and persistence properties of solutions to the Cauchy problem of the Fornberg-Whitham equation are considered respectively when the initial values are analytic or decaying. It is shown that the solutions of this equation are analytic in both variables, globally in space and locally in time. The solutions uniformly have the same decay property at any later time when the initial datum decays at infinity.

Key words: Fornberg-Whitham equation, analytic solutions, persistence property

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