A nonautonomous delayed viscoelastic wave equation with a linear damping: well-posedness and exponential stability

被引：0

作者：

Djemoui, Marwa ^{[1
]}

Chellaoua, Houria ^{[1
,2
]}

Boukhatem, Yamna ^{[1
,3
]}

机构：

[1] Univ Laghouat, Lab Pure & Appl Math, Laghouat, Algeria

[2] Univ Ghardaia, Dept Math & Comp Sci, Fac Sci & Technol, Ghardaia, Algeria

[3] Natl Higher Sch Math, Mahelma, Algeria

来源：

JOURNAL OF MATHEMATICAL MODELING | 2024年 / 12卷 / 02期

关键词：

Energy decay; global existence; Lyapunov functional; time delay; 2ND-ORDER EVOLUTION-EQUATIONS; GLOBAL EXISTENCE; ASYMPTOTIC STABILITY; INFINITE MEMORY; GENERAL DECAY; STABILIZATION; BOUNDARY; FEEDBACK; TERM; BEHAVIOR;

D O I：

10.22124/jmm.2024.26420.2331

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a nonautonomous viscoelastic wave equation with linear damping and delayed terms. Under some appropriate assumptions, we prove the global existence using the semi- group theory. Furthermore, for a small enough coefficient of delay, we obtained a stability result via a suitable Lyapunov function where the kernel function decays exponentially.

引用

页码：319 / 336

页数：18

共 46 条

[1] Well-posedness and stability results for some nonautonomous abstract linear hyperbolic equations with memory [J].

Al-Khulaifi, Waled ;

Diagana, Toka ;

Guesmia, Aissa .

SEMIGROUP FORUM, 2022, 105 (02) :351-373

[2] 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

[3] Feedback boundary stabilization of wave equations with interior delay [J].

Ammari, Kais ;

Nicaise, Serge ;

Pignotti, Cristina .

SYSTEMS & CONTROL LETTERS, 2010, 59 (10) :623-628

[4]

[Anonymous], 2002, Differential Integral Equations

[5]

Benaissa A, 2014, INT J DYN SYST DIFFE, V5, P1

[6] Feedback stabilization of a class of evolution equations with delay [J].

Benhassi, E. M. Ait ;

Ammari, K. ;

Boulite, S. ;

Maniar, L. .

JOURNAL OF EVOLUTION EQUATIONS, 2009, 9 (01) :103-121

[7] Existence and decay of solutions of a viscoelastic equation with a nonlinear source [J].

Berrimi, S ;

Messaoudi, SA .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (10) :2314-2331

[8]

Cavalcanti MM, 2002, ELECTRON J DIFFER EQ

[9] 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

[10]

Chellaoua H., 2020, Proc. Indian Acad. Sci. Math. Sci., V2, P7

← 1 2 3 4 5 →