General and optimal decay rates for a viscoelastic wave equation with strong damping

被引：0

作者：

Li, Qian ^{[1
]}

机构：

[1] Changzhi Univ, Dept Math, Changzhi 046011, Peoples R China

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 10期

关键词：

viscoelastic wave equation; strong damping; Lyapunov function; decay; GLOBAL EXISTENCE; BLOW-UP; UNIFORM DECAY; NONEXISTENCE;

D O I：

10.3934/math.20221006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work is devoted to investigating the decay properties for a nonlinear viscoelastic wave equation with strong damping. Under certain class of relaxation functions and initial data and using the perturbed energy method, we obtain general and optimal decay results.

引用

页码：18282 / 18296

页数：15

共 20 条

[1]

[Anonymous], 2003, RES MATH SCI

[2] Existence and uniform decay for a non-linear viscoelastic equation with strong damping [J].

Cavalcanti, MM ;

Cavalcanti, VND ;

Ferreira, J .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2001, 24 (14) :1043-1053

[3] GLOBAL EXISTENCE, UNIFORM DECAY AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING [J].

Chen, Hua ;

Liu, Gongwei .

ACTA MATHEMATICA SCIENTIA, 2013, 33 (01) :41-58

[4] Global well-posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping, linear strong damping and logarithmic nonlinearity [J].

Chen, Yuxuan ;

Xu, Runzhang .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 192

[5] Blow-up and global existence for solution of quasilinear viscoelastic wave equation with strong damping and source term [J].

Hao, Jianghao ;

Wei, Haiying .

BOUNDARY VALUE PROBLEMS, 2017,

[6] On decay and blow-up of solutions for a system of viscoelastic equations with weak damping and source terms [J].

He, Luofei .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019, 2019 (1)

[7] BLOW-UP FOR SEMILINEAR WAVE EQUATIONS WITH TIME-DEPENDENT DAMPING IN AN EXTERIOR DOMAIN [J].

Jleli, Mohamed ;

Samet, Bessem .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (07) :3885-3900

[8] INSTABILITY AND NONEXISTENCE OF GLOBAL SOLUTIONS TO NONLINEAR-WAVE EQUATIONS OF FORM PUTT = -AU + F(U) [J].

LEVINE, HA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 192 :1-21

[9] SOME ADDITIONAL REMARKS ON NONEXISTENCE OF GLOBAL SOLUTIONS TO NONLINEAR-WAVE EQUATIONS [J].

LEVINE, HA .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1974, 5 (01) :138-146

[10] Global nonexistence theorems for quasilinear evolution equations with dissipation [J].

Levine, HA ;

Serrin, J .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1997, 137 (04) :341-361

← 1 2 →