Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity

被引：14
|
作者：
Fujiwara, Kazumasa [1 ]
Ikeda, Masahiro [2 ]
Wakasugi, Yuta [3 ]
机构：
[1] Tohoku Univ, Math Inst, Aoba Ku, 6-3 Aoba, Sendai, Miyagi 9808578, Japan
[2] Keio Univ, Fac Sci & Technol, Dept Math, Ctr Adv Intelligence Project,RIKEN,Kohoku Ku, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan
[3] Ehime Univ, Grad Sch Sci & Engn, Dept Engn Prod & Environm, 3 Bunkyo Cho, Matsuyama, Ehime 7908577, Japan
来源：
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2019年 / 62卷 / 02期
基金：
日本学术振兴会;
关键词：
Damped wave equation; Lifespan estimate; Blow-up rate; ASYMPTOTIC PROFILES; SCALING VARIABLES; CRITICAL EXPONENT; GLOBAL-SOLUTIONS; CAUCHY-PROBLEM; LEQUATION; BEHAVIOR;
D O I：
10.1619/fesi.62.157
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study estimates of lifespan and blow-up rates of solutions for the Cauchy problem of the wave equation with a time -dependent damping and a power type non-linearity. When the damping acts on the solutions effectively, and the non linearity belongs to the subcritical case, we show the sharp lifespan estimates and the blow-up rates of solutions. The upper estimates are proved by an ODE argument, and the lower estimates are given by a method of scaling variables.
引用
收藏
页码：157 / 189
页数：33
相关论文
共 50 条
  • [31] REGULARITY AND SINGULARITY OF THE BLOW-UP CURVE FOR A WAVE EQUATION WITH A DERIVATIVE NONLINEARITY
    Sasaki, Takiko
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2018, 23 (5-6) : 373 - 408
  • [32] Blow-Up of Solutions for the Fourth-Order Schrödinger Equation with Combined Power-Type Nonlinearities
    Zhang, Zaiyun
    Wang, Dandan
    Chen, Jiannan
    Xie, Zihan
    Xu, Chengzhao
    JOURNAL OF GEOMETRIC ANALYSIS, 2024, 34 (10)
  • [33] Blow-up and lifespan of solutions for elastic membrane equation with distributed delay and logarithmic nonlinearity
    Boulaaras, Salah
    Jan, Rashid
    Choucha, Abdelbaki
    Zarai, Aderrahmane
    Benzahi, Mourad
    BOUNDARY VALUE PROBLEMS, 2024, 2024 (01)
  • [34] Blow-up and lifespan of solutions for elastic membrane equation with distributed delay and logarithmic nonlinearity
    Salah Boulaaras
    Rashid Jan
    Abdelbaki Choucha
    Aderrahmane Zaraï
    Mourad Benzahi
    Boundary Value Problems, 2024
  • [35] Blow-up for wave equation with weak boundary damping and source terms
    Ha, Tae Gab
    APPLIED MATHEMATICS LETTERS, 2015, 49 : 166 - 172
  • [36] Blow-up for the wave equation with nonlinear source and boundary damping terms
    Fiscella, Alessio
    Vitillaro, Enzo
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2015, 145 (04) : 759 - 778
  • [37] Sharp thresholds of blow-up and global existence for the Schrodinger equation with combined power-type and Choquard-type nonlinearities
    Wang, Yongbin
    Feng, Binhua
    BOUNDARY VALUE PROBLEMS, 2019, 2019 (01)
  • [38] Blow-up for semilinear wave equation with boundary damping and source terms
    Ha, Tae Gab
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 390 (01) : 328 - 334
  • [39] A blow-up result for a nonlinear wave equation with damping: The critical case
    Zhang, QS
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (02): : 109 - 114
  • [40] SMALL DATA BLOW-UP OF SEMI-LINEAR WAVE EQUATION WITH SCATTERING DISSIPATION AND TIME-DEPENDENT MASS
    Ikeda, Masahiro
    Tu, Ziheng
    Wakasa, Kyouhei
    EVOLUTION EQUATIONS AND CONTROL THEORY, 2022, 11 (02): : 515 - 536
12345