Blow-up of solutions for a viscoelastic wave equation with variable exponents

被引：32
|
作者：
Park, Sun-Hye [1 ]
Kang, Jum-Ran [2 ]
机构：
[1] Pusan Natl Univ, Ctr Educ Accreditat, Busan, South Korea
[2] Dong A Univ, Dept Math, Busan 604714, South Korea
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2019年 / 42卷 / 06期
基金：
新加坡国家研究基金会;
关键词：
blow-up; variable exponents; viscoelasticity; wave equation; INITIAL-ENERGY SOLUTIONS; GLOBAL EXISTENCE; NONEXISTENCE; SPACES;
D O I：
10.1002/mma.5501
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a viscoelastic wave equation with variable exponents: utt-Delta u+integral 0tg(t-s)Delta u(s)ds+a|ut|m(x)-2ut=b|u|p(x)-2u,where the exponents of nonlinearity p(center dot) and m(center dot) are given functions and a,b > 0 are constants. For nonincreasing positive function g, we prove the blow-up result for the solutions with positive initial energy as well as nonpositive initial energy. We extend the previous blow-up results to a viscoelastic wave equation with variable exponents.
引用
收藏
页码：2083 / 2097
页数：15
相关论文
共 50 条
  • [1] Viscoelastic plate equation with variable exponents: existence and blow-up
    Yilmaz, Nebi
    Piskin, Erhan
    Boulaaras, Salah
    JOURNAL OF ANALYSIS, 2024, 32 (5): : 2683 - 2708
  • [2] Blow-Up of Solutions for a Class Quasilinear Wave Equation with Nonlinearity Variable Exponents
    Tebba, Zakia
    Degaichia, Hakima
    Abdalla, Mohamed
    Cherif, Bahri Belkacem
    Mekawy, Ibrahim
    JOURNAL OF FUNCTION SPACES, 2021, 2021
  • [3] Blow-up of solutions of a nonlinear viscoelastic wave equation
    Song, Haitao
    Zhong, Chengkui
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (05) : 3877 - 3883
  • [4] Blow-up and decay of solutions for a viscoelastic Kirchhoff-type equation with distributed delay and variable exponents
    Choucha, Abdelbaki
    Boulaaras, Salah
    Jan, Rashid
    Alharbi, Rabab
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (08) : 6928 - 6945
  • [5] BLOW-UP OF SOLUTIONS TO A VISCOELASTIC WAVE EQUATION WITH NONLOCAL DAMPING
    Li, Donghao
    Zhang, Hongwei
    Liu, Shuo
    Hu, Qingiyng
    EVOLUTION EQUATIONS AND CONTROL THEORY, 2022, 11 (06): : 2017 - 2031
  • [6] Blow-up solutions of a time-fractional diffusion equation with variable exponents
    Manimaran, J.
    Shangerganesh, L.
    TBILISI MATHEMATICAL JOURNAL, 2019, 12 (04) : 149 - 157
  • [7] BLOW-UP AND DECAY OF SOLUTIONS FOR A DELAYED TIMOSHENKO EQUATION WITH VARIABLE-EXPONENTS
    Yueksekkaya, Hazal
    Piskin, Erhan
    MISKOLC MATHEMATICAL NOTES, 2022, 23 (02) : 1001 - 1022
  • [8] Blow-up of solutions for a semi-linear heat equation with variable exponents
    Zhang, Jibing
    Gao, Yunzhu
    MANUFACTURING PROCESS AND EQUIPMENT, PTS 1-4, 2013, 694-697 : 699 - +
  • [9] Decay and blow-up for a viscoelastic wave equation of variable coefficients with logarithmic nonlinearity
    Hao, Jianghao
    Du, Fangqing
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 506 (01)
  • [10] On a Viscoelastic Plate Equation with Logarithmic Nonlinearity and Variable-Exponents: Global Existence, General Decay and Blow-Up of Solutions
    Choucha, Abdelbaki
    Boulaaras, Salah
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2024, 50 (04)
12345