Global solutions and blow-up phenomena for the periodic b-equation

被引：17
|
作者：
Zhang, S. [1 ]
Yin, Z. [1 ]
机构：
[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
来源：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2010年 / 82卷
关键词：
DEGASPERIS-PROCESI EQUATION; SHALLOW-WATER EQUATION; CAMASSA-HOLM EQUATION; KORTEWEG-DEVRIES EQUATION; WELL-POSEDNESS; INTEGRABLE EQUATION; PEAKON SOLUTIONS; WEAK SOLUTIONS; CAUCHY-PROBLEM; WAVE SOLUTIONS;
D O I：
10.1112/jlms/jdq044
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the paper, we mainly study the Cauchy problem of a family of asymptotically equivalent shallow water wave equations, the so called periodic b-equation. We first establish the local well-posedness for the periodic b-equation. Then we derive the precise blow-up scenario and present two blow-up results. Moreover, we show that the periodic b-equation has global strong solutions. Finally, we prove the existence of global weak solutions to the periodic b-equation, provided that initial data satisfy certain sign conditions.
引用
收藏
页码：482 / 500
页数：19
相关论文
共 50 条
  • [21] On the blow-up of solutions of the periodic Camassa-Holm equation
    Yin, ZY
    [J]. DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2005, 12 (3-4): : 375 - 381
  • [22] On the blow-up of solutions to the periodic Caniassa-Holm equation
    Wahlen, Erik
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2007, 13 (5-6): : 643 - 653
  • [23] On the blow-up of solutions to the periodic Camassa-Holm equation
    Erik Wahlén
    [J]. Nonlinear Differential Equations and Applications NoDEA, 2007, 13 : 643 - 653
  • [24] Global existence and blow-up phenomena for a periodic 2-component Camassa-Holm equation
    Hu, Qiaoyi
    Yin, Zhaoyang
    [J]. MONATSHEFTE FUR MATHEMATIK, 2012, 165 (02): : 217 - 235
  • [25] Blow-up phenomena and global existence for the weakly dissipative generalized periodic Degasperis-Procesi equation
    Caochuan Ma
    Ahmed Alsaedi
    Tasawar Hayat
    Yong Zhou
    [J]. Boundary Value Problems, 2014
  • [26] Blow-up phenomena and global existence for the weakly dissipative generalized periodic Degasperis-Procesi equation
    Ma, Caochuan
    Alsaedi, Ahmed
    Hayat, Tasawar
    Zhou, Yong
    [J]. BOUNDARY VALUE PROBLEMS, 2014,
  • [27] Global existence and blow-up phenomena for the weakly dissipative Novikov equation
    Yan, Wei
    Li, Yongsheng
    Zhang, Yimin
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) : 2464 - 2473
  • [28] Global existence and blow-up phenomena for the Degasperis-Procesi equation
    Liu, Yue
    Yin, Zhaoyang
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 267 (03) : 801 - 820
  • [29] BLOW-UP PHENOMENA AND TRAVELLING WAVE SOLUTIONS TO THE PERIODIC INTEGRABLE DISPERSIVE HUNTER-SAXTON EQUATION
    Li, Min
    Yin, Zhaoyang
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (12): : 6471 - 6485
  • [30] Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation
    Yue Liu
    Zhaoyang Yin
    [J]. Communications in Mathematical Physics, 2006, 267 : 801 - 820
12345