BLOW-UP OF SOLUTION FOR A VISCOELASTIC WAVE EQUATION WITH DELAY

被引：10
|
作者：
Wu, Shun-Tang [1 ]
机构：
[1] Natl Taipei Univ Technol, Gen Educ Ctr, Taipei 106, Taiwan
来源：
ACTA MATHEMATICA SCIENTIA | 2019年 / 39卷 / 01期
关键词：
blow up; nonlinear source; wave equation; delay; viscoelastic; TIME-VARYING DELAY; DYNAMIC BOUNDARY; GENERAL DECAY; STABILIZATION; STABILITY; RESPECT; SYSTEMS; TERM;
D O I：
10.1007/s10473-019-0124-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the following viscoelastic wave equation with delay vertical bar ut vertical bar(rho) u(tt) - Delta u - Delta u(tt) + integral(t)(0) g(t - s)Delta u(s)ds + mu(1)u(t)(x, t) + mu(2)u(t)(x,t - tau ) = b vertical bar u vertical bar(p-2) u in a bounded domain. Under appropriate conditions on mu(1), mu(2), the kernel function g, the nonlinear source and the initial data, there are solutions that blow up in finite time.
引用
收藏
页码：329 / 338
页数：10
相关论文
共 50 条
  • [21] Bounds for the blow-up time of solution to a nonlinear viscoelastic equation with fractional damping
    Rayappan, Saranya
    Aruchamy, Akilandeeswari
    Natarajan, Annapoorani
    INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL, 2024, 12 (01) : 167 - 179
  • [22] Blow-up phenomena for a viscoelastic wave equation with strong damping and logarithmic nonlinearity
    Ha, Tae Gab
    Park, Sun-Hye
    ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [23] Bounds for the blow-up time of solution to a nonlinear viscoelastic equation with fractional damping
    Saranya Rayappan
    Akilandeeswari Aruchamy
    Annapoorani Natarajan
    International Journal of Dynamics and Control, 2024, 12 (1) : 167 - 179
  • [24] Blow-up of solutions for a viscoelastic equation with nonlinear damping
    Yang Zhifeng
    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2008, 6 (04): : 568 - 575
  • [25] Blow-Up of Solutions for a Singular Nonlocal Viscoelastic Equation
    Wu Shuntang
    JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2011, 24 (02): : 140 - 149
  • [26] GROWTH AND BLOW-UP OF VISCOELASTIC WAVE EQUATION SOLUTIONS WITH LOGARITHMIC SOURCE, ACOUSTIC AND FRACTIONAL CONDITIONS, AND NONLINEAR BOUNDARY DELAY
    Choucha, Abdelbaki
    Haiour, Mohamed
    Jan, Rashid
    Shahrouzi, Mohammad
    Agarwal, Praveen
    Abdalla, Mohamed
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2025,
  • [27] BLOW-UP OF SOLUTIONS TO A NONLINEAR WAVE EQUATION
    Georgiev, Svetlin Georgiev
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2004,
  • [28] Blow-up of solution for a generalized Boussinesq equation
    王艳萍
    郭柏灵
    AppliedMathematicsandMechanics(EnglishEdition), 2007, (11) : 1437 - 1443
  • [29] ASYMPTOTIC BEHAVIOR AND BLOW-UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATION WITH BOUNDARY DISSIPATION
    Tahamtani, Faramarz
    Peyravi, Amir
    TAIWANESE JOURNAL OF MATHEMATICS, 2013, 17 (06): : 1921 - 1943
  • [30] Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strong damping
    Peng, Xiaoming
    Shang, Yadong
    Zheng, Xiaoxiao
    APPLIED MATHEMATICS LETTERS, 2018, 76 : 66 - 73
12345