两个分支的Degasperis-Procesi系统的弱适定性  

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

作　　者：陈丽娜 关春霞[1] 冯兆永[2] 刘成霞 CHEN Lina;GUAN Chunxia;FENG Zhaoyong;LIU Chengxia(School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;Stomatological Hospital, Southern Medical University, Guangzhou 510280, China)

机构地区：[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

出　　处：《中山大学学报（自然科学版）》2019年第1期131-137,共7页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11471339);广东省高校特色创新类项目(2016KTSCX028);广东省医学科研基金(A2018339);南方医科大学口腔医院科研培育计划(PY2017017);广州市科技计划(201607010144)

摘　　要：研究两个分支的Degasperis-Procesi系统Cauchy问题当初值(u0,ρ0)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。The weak well-posedness for the Cauchy problem of the two-component Degasperis-Procesi system with the initial value (u 0,ρ 0)∈(H 1( R )∩W 1,∞( R ))×(L 2( 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.

关 键 词：两个分支的Degasperis-Procesi方程 存在唯一性 弱连续依赖性 

分 类 号：O175[理学—数学]