中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (1): 131-137.doi: 10.13471/j.cnki.acta.snus.2019.01.016

• 论文 • 上一篇    下一篇

两个分支的Degasperis-Procesi系统的弱适定性

陈丽娜1,关春霞1, 冯兆永2,刘成霞3   

  1. 1. 广东工业大学应用数学学院,广东 广州 510520;
    2. 中山大学数学学院,广东 广州 510275;
    3. 南方医科大学口腔医院,广东 广州 510280
  • 收稿日期:2018-07-26 出版日期:2019-01-25 发布日期:2019-01-25
  • 通讯作者: 关春霞(1981年生),女;研究方向:偏微分方程;E-mail:guanchunxia123@163.com 冯兆永(1977年生),男;研究方向:偏微分方程;E-mail:fzhaoy@mail.sysu.edu.cn

Weak well-posedness for the two component Degasperis-Procesi system

CHEN Lina1, GUAN Chunxia1, FENG Zhaoyong2, LIU Chengxia3   

  1. 1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;
    2. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
    3. Stomatological Hospital, Southern Medical University, Guangzhou 510280, China
  • Received:2018-07-26 Online:2019-01-25 Published:2019-01-25

摘要:

研究两个分支的Degasperis-Procesi系统Cauchy问题当初值(u00)在空间(H1(R)∩W1,∞(R))×(L2(R)∩L(R))时解的弱适定性问题。首先,利用特征线方法,把两个分支的Degasperis-Procesi系统化成一个ODE系统。其次,应用经典的常微分方程解的适定性理论,得到ODE系统解的存在唯一性。最后证明了两个分支的Degasperis-Procesi系统解的存在唯一性并给出解对初值的弱连续依赖性结论。

关键词: 两个分支的Degasperis-Procesi方程, 存在唯一性, 弱连续依赖性

Abstract:

The weak well-posedness for the Cauchy problem of the twocomponent DegasperisProcesi system with the initial value(u00)∈(H1(R)∩W1,∞(R))×(L2(R)∩L(R))is obtained. First, by introducing characteristics, the two-component Degasperis-Procesi systems are transformed into an ODE system. Next, applying the classic well-posedness theory to the solution of ordinary differential equations, the local existence and uniqueness of the solution to the ODE system are obtained. Finally, the local existence and uniqueness of the solution for the two-component Degasperis-Procesi system are investigated. And the conclusion of the weak continuous dependence on initial conditions is proven.

Key words: two-component Degasperis-Procesi system, existence and uniqueness, weak continuous dependence

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