General decay and blow-up of solutions for a nonlinear viscoelastic wave equation with strong damping

被引：13

作者：

Li, Qian ^{[1
]}

He, Luofei ^{[1
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2018年

关键词：

Viscoelastic wave equation; Strong damping; General decay; Blow up; INITIAL-ENERGY SOLUTIONS; GLOBAL EXISTENCE; WELL-POSEDNESS; RATES;

D O I：

10.1186/s13661-018-1072-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is concerned with the decay and blow-up properties of a nonlinear viscoelastic wave equation with strong damping. We first show a local existence theorem. Then, we prove the global existence of solutions and establish a general decay rate estimate. Finally, we show the finite time blow-up result for some solutions with negative initial energy and positive initial energy.

引用

页数：22

共 50 条

[1] General decay and blow-up of solutions for a nonlinear viscoelastic wave equation with strong damping
Qian Li
Luofei He
Boundary Value Problems, 2018
[2] BLOW-UP AND GENERAL DECAY OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC EQUATION
Chen, Wenying
Xiong, Yangping
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
[3] Blow-up of solutions for a viscoelastic equation with nonlinear damping
Yang Zhifeng
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2008, 6 (04): : 568 - 575
[4] Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping
Fei Liang
Hongjun Gao
Boundary Value Problems, 2011
[5] Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping
Liang, Fei
Gao, Hongjun
BOUNDARY VALUE PROBLEMS, 2011,
[6] General decay and blow-up of solution for a viscoelastic wave equation with nonlinear degenerate damping and source terms
Yin, Ziyang
Wang, Shubin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 531 (01)
[7] General decay and blow-up of solutions for a viscoelastic equation with nonlinear boundary damping-source interactions
Wu, Shun-Tang
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2012, 63 (01): : 65 - 106
[8] General decay and blow-up of solutions for a viscoelastic equation with nonlinear boundary damping-source interactions
Shun-Tang Wu
Zeitschrift für angewandte Mathematik und Physik, 2012, 63 : 65 - 106
[9] Blow-up of solutions of a nonlinear viscoelastic wave equation
Song, Haitao
Zhong, Chengkui
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (05) : 3877 - 3883
[10] 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

← 1 2 3 4 5 →