Well-posedness and global existence for a generalized Degasperis-Procesi equation

被引：24
|
作者：
Li, Jinlu [1 ]
Yin, Zhaoyang [1 ,2 ]
机构：
[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
[2] Macau Univ Sci & Technol, Fac Informat Technol, Macau, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2016年 / 28卷
关键词：
A generalized Degasperis-Procesi equation; Littlewood-Paley theory; Local well-posedness; Blow-up criterion; Global existence; SHALLOW-WATER EQUATION; CAUCHY-PROBLEM; WEAK SOLUTIONS; INTEGRABLE EQUATION; WAVE SOLUTIONS; TRAJECTORIES; BREAKING;
D O I：
10.1016/j.nonrwa.2015.09.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We first establish the local existence and uniqueness of strong solutions for the Cauchy problem of a generalized Degasperis-Procesi equation in nonhomogeneous Besov spaces by using the Littlewood-Paley theory. Then, we prove the solution depends continuously on the initial data. Finally, we derive a blow-up criterion and present a global existence result for the equation. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：72 / 90
页数：19
相关论文
共 50 条
  • [31] On the Existence of Solitary Wave Solutions for Perturbed Degasperis-Procesi Equation
    Xu, Guoan
    Zhang, Yi
    [J]. QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2021, 20 (03)
  • [32] On the Existence of Solitary Wave Solutions for Perturbed Degasperis-Procesi Equation
    Guoan Xu
    Yi Zhang
    [J]. Qualitative Theory of Dynamical Systems, 2021, 20
  • [33] Smooth travelling wave solutions in a generalized Degasperis-Procesi equation
    Zhu, Kun
    Shen, Jianhe
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2021, 98
  • [34] Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation
    Zhou, Jiangbo
    Tian, Lixin
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2009, 2009
  • [35] The Stability of Solutions for the Generalized Degasperis-Procesi Equation with Variable Coefficients
    Chen, Jing
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2015, 2015
  • [36] On the L1 Stability to a Generalized Degasperis-Procesi Equation
    Yan, Haibo
    Yong, Ls
    Hu, Hanlei
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [37] GLOBAL EXISTENCE AND BLOW-UP PHENOMENA FOR A WEAKLY DISSIPATIVE DEGASPERIS-PROCESI EQUATION
    Wu, Shuyin
    Escher, Joachim
    Yin, Zhaoyang
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2009, 12 (03): : 633 - 645
  • [38] Variational Iteration Method for Solving the Generalized Degasperis-Procesi Equation
    Qian Lijuan
    Tian Lixin
    Ma Kaiping
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [39] Non-uniform dependence for a generalized Degasperis-Procesi equation
    Gui, Shaohui
    Li, Jinlu
    Zhu, Weipeng
    [J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2019, 198 (03) : 803 - 810
  • [40] Exact solutions to Degasperis-Procesi equation
    Zhang Lin-Na
    Fu Zun-Tao
    Liu Shi-Kuo
    [J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2008, 50 (01) : 48 - 50
12345