Degasperis-Procesi方程的弱适定性  

Weak well-posedness for a Degasperis-Procesi equation

作　　者：王健鸣 冯兆永[2] 刘成霞 WANG Jianming;FENG Zhaoyong;LIU Chengxia(School of Applied Mathematics,Guangdong University of Technology,Guangzhou 510520,China;School of Mathematics,Sun Yat-sen University,Guangzhou 510275,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）》2018年第4期86-91,共6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);广州市科技计划(201607010144);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)

摘　　要：研究Degasperis-Procesi方程Cauchy问题当初值u_0∈H^1(R)∩W^(1,∞)(R)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。The weak well-posedness is obtained for the Cauchy problem of the Degasperis-Procesi equation with the initial value u0∈H1 （R）∩W1,∞ （R）. 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 

分 类 号：O175[理学—数学]