Blow-up solutions for a case of b-family equations

被引：0
|
作者：
Zongguang Li
Rui Liu
机构：
[1] South China University of Technology,School of Mathematics
来源：
Acta Mathematica Scientia | 2020年 / 40卷
关键词：
-family equation; blow-up solutions; qualitative theory; bifurcation method; 34A20; 34C35; 35B65; 58F05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this article, we study the blow-up solutions for a case of b-family equations. Using the qualitative theory of differential equations and the bifurcation method of dynamical systems, we obtain five types of blow-up solutions: the hyperbolic blow-up solution, the fractional blow-up solution, the trigonometric blow-up solution, the first elliptic blow-up solution, and the second elliptic blow-up solution. Not only are the expressions of these blow-up solutions given, but also their relationships are discovered. In particular, it is found that two bounded solitary solutions are bifurcated from an elliptic blow-up solution.
引用
收藏
页码：910 / 920
页数：10
相关论文
共 50 条
  • [41] BLOW-UP OF SOLUTIONS FOR SEMILINEAR FRACTIONAL SCHRODINGER EQUATIONS
    Fino, A. Z.
    Dannawi, I.
    Kirane, M.
    JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2018, 30 (01) : 67 - 80
  • [42] Blow-up criterion of smooth solutions for the Boussinesq equations
    Ye, Zhuan
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 110 : 97 - 103
  • [43] BLOW-UP OF SOLUTIONS OF HAMILTON-JACOBI EQUATIONS
    FRIEDMAN, A
    SOUGANIDIS, PE
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1986, 11 (04) : 397 - 443
  • [44] BLOW-UP OF SOLUTIONS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS
    FRIEDMAN, A
    MCLEOD, B
    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1986, 96 (01) : 55 - 80
  • [45] THE SOLUTIONS FOR THE EQUATIONS WITH LOCALIZED CONSISTENT BLOW-UP RATE
    Chen, Miaochao
    Shi, Jizhong
    Chen, Peishu
    2011 3RD INTERNATIONAL CONFERENCE ON COMPUTER TECHNOLOGY AND DEVELOPMENT (ICCTD 2011), VOL 1, 2012, : 55 - 59
  • [46] Numerical diagnosis of blow-up of solutions of pseudoparabolic equations
    A. B. Al’shin
    E. A. Al’shina
    Journal of Mathematical Sciences, 2008, 148 (1) : 143 - 162
  • [47] Behavior of blow-up solutions for quasilinear parabolic equations
    Yevgenieva Y.A.
    Journal of Mathematical Sciences, 2020, 249 (5) : 804 - 816
  • [48] BLOW-UP SOLUTIONS FOR N COUPLED SCHRODINGER EQUATIONS
    Chen, Jianqing
    Guo, Boling
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
  • [49] Blow-up rates of large solutions for elliptic equations
    Zhang, Zhijun
    Ma, Yunjie
    Mi, Ling
    Li, Xiaohong
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (01) : 180 - 199
  • [50] Blow-up of solutions to cubic nonlinear Schrodinger equations with defect: The radial case
    Goubet, Olivier
    Hamraoui, Emna
    ADVANCES IN NONLINEAR ANALYSIS, 2017, 6 (02) : 183 - 197
12345