Weak well-posedness for a Degasperis-Procesi equation

WANG Jianming; FENG Zhaoyong; LIU Chengxia

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Weak well-posedness for a Degasperis-Procesi equation

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- Weak well-posedness for a Degasperis-Procesi equation
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 57, Issue 4, Pages: 86-91(2018)
- 作者机构：
  
  1. 广东工业大学应用数学学院,广东,广州,510520
  2. 
  3. 中山大学数学学院,广东,广州,510275
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2018，
  
  Published Online：25 July 2018，
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WANG Jianming, FENG Zhaoyong, LIU Chengxia. Weak well-posedness for a Degasperis-Procesi equation. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(4):86-91(2018)
DOI：

WANG Jianming, FENG Zhaoyong, LIU Chengxia. Weak well-posedness for a Degasperis-Procesi equation. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(4):86-91(2018) DOI：

摘要

研究 Degasperis-Procesi 方程 Cauchy 问题当初值

∈H

(

)∩

1，∞

(

)时解的弱适定性。首先运用特征线将 Degasperis-Procesi 方程的Cauchy问题转化成一个ODE系统，其次利用ODE理论证明该ODE系统的解存在唯一，最后利用该ODE系统与原方程的关系，研究原方程解的存在唯一性，并给出原方程的解对初值的弱连续依赖性。

Abstract

The weak well-posedness is obtained for the Cauchy problem of the Degasperis-Procesi equation with the initial value

∈H

(

)∩

1，∞

(

). At first，by introducing the characteristics，the Cauchy problem of the Degasperis-Procesi equation is transformed into an ODE system. By using the ODE theory，the local existence and uniqueness of the solution to the ODE system is proved. Finally，the unique solution is investigated for the original equation by the relationship between the original equation and the ODE system，and the weak continuous dependence on initial conditions to the original equation is given.

关键词

Degasperis-Procesi方程弱适定性特征线弱连续依赖性

Keywords

Degasperis-Procesi equationweak well-posednesscharacteristicsweak continuous dependence

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Related Institution

Department of Mathematics and Information Science， Zhengzhou University of Light Industry

Department of Mathematics, South China Agricultural University

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