BLOW-UP FOR THE EULER-BERNOULLI VISCOELASTIC EQUATION WITH A NONLINEAR SOURCE

被引：0

作者：

Yang, Zhifeng ^{[1
,2
]}

Fan, Guobing ^{[3
]}

机构：

[1] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China

[2] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China

[3] Hunan Univ Finance & Econ, Changsha 410205, Hunan, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年

关键词：

Viscoelastic equation; blow-up; nonlinear source; GLOBAL EXISTENCE; WAVE-EQUATION; NONEXISTENCE; SYSTEM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider the Euler-Bernoulli viscoelastic equation u(tt)(x,t) + Delta(2)u(x,t) - integral(t)(0) g(t-s)Delta(2)u(x,s)ds = vertical bar u vertical bar(p-1)u together with some suitable initial data and boundary conditions in Omega x (0, +infinity). Some sufficient conditions on blow-up of solutions are obtained under different initial energy states. And from these results we can clearly understand the competitive relationship between the viscoelastic damping and source.

引用

页数：12

共 50 条

[31] 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
[32] A lower bound for the blow-up time to a viscoelastic hyperbolic equation with nonlinear sources
Guo, Bin
Liu, Fang
APPLIED MATHEMATICS LETTERS, 2016, 60 : 115 - 119
[33] 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
[34] General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source
Liu, Wenjun
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (06) : 1890 - 1904
[35] Blow-up phenomenon for a nonlinear wave equation with anisotropy and a source term
Khelghati, Ali
Baghaei, Khadijeh
APPLICABLE ANALYSIS, 2020, 99 (03) : 462 - 478
[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] Blow-up behavior for a nonlinear heat equation with a localized source in a ball
Fukuda, I
Suzuki, R
JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 218 (02) : 273 - 291
[38] BLOW-UP OF SOLUTIONS FOR AN INTEGRO-DIFFERENTIAL EQUATION WITH A NONLINEAR SOURCE
Wu, Shun-Tang
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2006,
[39] Global existence and blow-up of solutions for higher-order viscoelastic wave equation with a nonlinear source term
Ye, Yaojun
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 112 : 129 - 146
[40] Control of a viscoelastic translational Euler-Bernoulli beam
Berkani, Amirouche
Tatar, Nasser-eddine
Khemmoudj, Ammar
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (01) : 237 - 254

← 1 2 3 4 5 →