BLOW-UP OF SOLUTIONS TO A NONLINEAR WAVE EQUATION

被引：0
|
作者：
Georgiev, Svetlin Georgiev [1 ]
机构：
[1] Univ Sofia, Fac Math & Informat, Dept Differential Equat, Sofia, Bulgaria
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2004年
关键词：
Wave equation; blow-up; hyperbolic space;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the solutions to the the radial 2-dimensional wave equation [GRAPHICS] where r = vertical bar x vertical bar and x in R-2. We show that this Cauchy problem, with values into a hyperbolic space, is ill posed in subcritical Sobolev spaces. In particular, we construct a function g(t, r) in the space L-p([ 0, 1] L-rad(q)), with 1/p + 2/q = 3-gamma, 0 < gamma < 1, p >= 1, and 1 < q <= 2, for which the solution satisfies lim(t) (-> 0) parallel to(chi) over bar parallel to(H) over dot(rad)(gamma) = infinity. In doing so, we provide a counterexample to estimates in [1].
引用
收藏
页数：7
相关论文
共 50 条
  • [1] Blow-up of solutions of a nonlinear viscoelastic wave equation
    Song, Haitao
    Zhong, Chengkui
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (05) : 3877 - 3883
  • [2] On the computation for blow-up solutions of the nonlinear wave equation
    Cho, Chien-Hong
    [J]. NUMERISCHE MATHEMATIK, 2018, 138 (03) : 537 - 556
  • [3] On the computation for blow-up solutions of the nonlinear wave equation
    Chien-Hong Cho
    [J]. Numerische Mathematik, 2018, 138 : 537 - 556
  • [4] Global existence and blow-up of solutions for a nonlinear wave equation with memory
    Liang, Fei
    Gao, Hongjun
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012,
  • [5] A REMARK ON BLOW-UP SOLUTIONS FOR NONLINEAR WAVE EQUATION WITH WEIGHTED NONLINEARITIES
    Alarfaj, Thanaa
    Aljaber, Noha
    Alshammari, Manal
    Majdoub, Mohamed
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS, 2019, 10 (06): : 69 - 78
  • [6] Global existence and blow-up of solutions for a nonlinear wave equation with memory
    Fei Liang
    Hongjun Gao
    [J]. Journal of Inequalities and Applications, 2012
  • [7] Solutions with Prescribed Local Blow-up Surface for the Nonlinear Wave Equation
    Cazenave, Thierry
    Martel, Yvan
    Zhao, Lifeng
    [J]. ADVANCED NONLINEAR STUDIES, 2019, 19 (04) : 639 - 675
  • [8] BLOW-UP OF SOLUTIONS FOR A NONLINEAR WAVE EQUATION WITH NONNEGATIVE INITIAL ENERGY
    Liu, Wenjun
    Sun, Yun
    Li, Gang
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
  • [9] Blow-up of solutions of the nonlinear Sobolev equation
    Cao, Yang
    Nie, Yuanyuan
    [J]. APPLIED MATHEMATICS LETTERS, 2014, 28 : 1 - 6
  • [10] Blow-up solutions for a nonlinear wave equation with boundary damping and interior source
    Feng, Hongyinping
    Li, Shengjia
    Zhi, Xia
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) : 2273 - 2280
12345