On similarity solutions and blow-up spectra for a semilinear wave equation

被引：11

作者：

Galaktionov, VA ^{[1
]}

Pohozaev, SI

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] MV Keldysh Appl Math Inst, Moscow 125047, Russia

[3] VA Steklov Math Inst, Moscow 117966, Russia

来源：

QUARTERLY OF APPLIED MATHEMATICS | 2003年 / 61卷 / 03期

关键词：

semilinear wave equation; blow-up; asymptotic behaviour; similarity solutions; fibering method; quadratic pencil; eigenvalue problem;

D O I：

10.1090/qam/1999839

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct countable spectra of different asymptotic patterns of self-similar and approximate self-similar types for global and blow-up solutions for the semi-linear wave equation u(tt) = Deltau + \u\(p-1)u, x is an element of R-N, t > 0, in different ranges of exponent p and dimension N.

引用

页码：583 / 600

页数：18

共 50 条

[21] THE BLOW-UP AND LIFESPAN OF SOLUTIONS TO SYSTEMS OF SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENTS IN HIGH DIMENSIONS
Kurokawa, Yuki
Takamura, Hiroyuki
Wakasa, Kyouhei
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2012, 25 (3-4) : 363 - 382
[22] Blow-up for semilinear wave equation with boundary damping and source terms
Ha, Tae Gab
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 390 (01) : 328 - 334
[23] A lower bound for the blow-up time to a damped semilinear wave equation
Sun, Lili
Guo, Bin
Gao, Wenjie
[J]. APPLIED MATHEMATICS LETTERS, 2014, 37 : 22 - 25
[24] BLOW-UP PROFILE FOR THE COMPLEX-VALUED SEMILINEAR WAVE EQUATION
Azaiez, Asma
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 367 (08) : 5891 - 5933
[25] Blow-up at infinity of solutions to a semilinear heat equation with logarithmic nonlinearity
Han, Yuzhu
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 474 (01) : 513 - 517
[26] 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
[27] Blow-up of positive solutions of a semilinear parabolic equation with a gradient term
Chlebík, M
Fila, M
Quittner, P
[J]. DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2003, 10 (04): : 525 - 537
[28] On the computation for blow-up solutions of the nonlinear wave equation
Cho, Chien-Hong
[J]. NUMERISCHE MATHEMATIK, 2018, 138 (03) : 537 - 556
[29] On the computation for blow-up solutions of the nonlinear wave equation
Chien-Hong Cho
[J]. Numerische Mathematik, 2018, 138 : 537 - 556
[30] Blow-up of solutions to semilinear wave equations with variable coefficients and boundary
Zhou, Yi
Han, Wei
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 374 (02) : 585 - 601

← 1 2 3 4 5 →