On general decay for a nonlinear viscoelastic equation

被引：4

作者：

Kelleche, Abdelkarim ^{[1
]}

Feng, Baowei ^{[2
]}

机构：

[1] Univ Djilali Bounaama, Fac Sci & Technol, Soufay, Khemis Miliana, Algeria

[2] Southwestern Univ Finance & Econ, Dept Econ Math, Chengdu, Peoples R China

来源：

APPLICABLE ANALYSIS | 2023年 / 102卷 / 06期

关键词：

Energy decay; multiplier technique; wave equation; convexity; EXPONENTIAL STABILITY; LINEAR VISCOELASTICITY; ASYMPTOTIC STABILITY; EXISTENCE; BEHAVIOR; ENERGY;

D O I：

10.1080/00036811.2021.1992394

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with a nonlinear viscoelastic equation. The aim is to expand the class of the function of relaxation h(t) that ensuring a general decay. We adopt the following commonly condition on relaxation function h '(t) <= -xi(t)chi(h(t)), where xi is a nonincreasing function and chi is an increasing and convex function on the whole [0, infinity) instead of is convex only near the origin in the literature.

引用

页码：1582 / 1600

页数：19

共 28 条

[1] Decay estimates for second order evolution equations with memory [J].

Alabau-Boussouira, Fatiha ;

Cannarsa, Piermarco ;

Sforza, Daniela .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (05) :1342-1372

[2] A general method for proving sharp energy decay rates for memory-dissipative evolution equations [J].

Alabau-Boussouira, Fatiha ;

Cannarsa, Piermarco .

COMPTES RENDUS MATHEMATIQUE, 2009, 347 (15-16) :867-872

[3]

[Anonymous], 1992, SIAM Studies in Applied Mathematics

[4]

Cavalcanti M.M., 2001, Diff. Integ. Eqs, V14, P85

[5] Intrinsic decay rates for the energy of a nonlinear viscoelastic equation modeling the vibrations of thin rods with variable density [J].

Cavalcanti, Marcelo M. ;

Domingos Cavalcanti, Valeria N. ;

Lasiecka, Irena ;

Webler, Claudete M. .

ADVANCES IN NONLINEAR ANALYSIS, 2017, 6 (02) :121-145

[6] Existence and sharp decay rate estimates for a von Karman system with long memory [J].

Cavalcanti, Marcelo M. ;

Cavalcanti, Andre D. D. ;

Lasiecka, Irena ;

Wang, Xiaojun .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 22 :289-306

[7] 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

[8]

Cavalcanti MM., 2001, DISCRETE CONTIN DYN, V19, P2012

[9] General decay properties of abstract linear viscoelasticity [J].

Conti, Monica ;

Pata, Vittorino .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2019, 71 (01)

[10]

DAFERMOS CM, 1970, ARCH RATION MECH AN, V37, P297

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