Asymptotic behavior of a viscoelastic wave equation with a delay in internal fractional feedback

被引：6
|
作者：
Aounallah, Radhouane [1 ]
Choucha, Adbelbaki [2 ,3 ]
Boulaaras, Salah [4 ]
Zarai, Abderrahmane [5 ]
机构：
[1] Univ Djillali Liabes Sidi Bel Abbes, Dept Math, Sidi Bell Abbas, Algeria
[2] Amar Teleji Laghouat Univ, Fac Sci, Dept Mat Sci, Laghouat, Algeria
[3] Ghardaia Univ, Lab Math & Appl Sci, Ghardaia, Algeria
[4] Qassim Univ, Coll Sci, Dept Math, Buraydah 51452, Saudi Arabia
[5] Larbi Tebessi Univ, Lab Math Informat & Syst LAMIS, Dept Math & Comp Sci, Tebessa 12002, Algeria
来源：
ARCHIVES OF CONTROL SCIENCES | 2024年 / 34卷 / 02期
关键词：
global existence; general decay; relaxation function; delay fractional feedback; partial differential equations; GENERAL DECAY; ENERGY DECAY; BLOW-UP; BOUNDARY; STABILIZATION; EXISTENCE; SYSTEMS;
D O I：
10.24425/acs.2024.149665
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We consider the viscoelastic wave equation with a time delay term in internal fractional feedback. By employing the energy method along with the Faedo-Galerkin procedure, we establish the global existence of solutions, subject to certain conditions. Additionally, we demonstrate how appropriate Lyapunov functionals can lead to general decay results of the energy.
引用
收藏
页码：379 / 413
页数：35
相关论文
共 50 条
  • [41] Asymptotic Behavior for High Moments of the Fractional Heat Equation with Fractional Noise
    Litan Yan
    Xianye Yu
    Journal of Theoretical Probability, 2019, 32 : 1617 - 1646
  • [42] Results on a nonlinear wave equation with acoustic and fractional boundary conditions coupling by logarithmic source and delay terms: Global existence and asymptotic behavior of solutions
    Choucha, Abdelbaki
    Boulaaras, Salah
    Yazid, Fares
    Jan, Rashid
    Mekawy, Ibrahim
    RESULTS IN APPLIED MATHEMATICS, 2024, 24
  • [43] ASYMPTOTIC ANALYSIS OF THE FORCED INTERNAL GRAVITY WAVE EQUATION
    Rees, Tim
    Lamb, Kevin G.
    Poulin, Francis J.
    SIAM JOURNAL ON APPLIED MATHEMATICS, 2012, 72 (04) : 1041 - 1060
  • [44] Existence and global asymptotic behavior of S-asymptotically periodic solutions for fractional evolution equation with delay
    Li, Qiang
    Liu, Lishan
    Wu, Xu
    NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2023, 28 (05): : 906 - 931
  • [45] Global existence and asymptotic behavior for a fractional differential equation
    Messaoudi, Salim A.
    Said-Houari, Belkacem
    Tatar, Nasser-eddine
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (02) : 1955 - 1962
  • [46] Existence, uniqueness and asymptotic behavior of traveling wave fronts for a generalized Fisher equation with nonlocal delay
    Wei, Jingdong
    Tian, Lixin
    Zhou, Jiangbo
    Zhen, Zaili
    CHAOS SOLITONS & FRACTALS, 2017, 103 : 536 - 543
  • [47] Asymptotic behavior of a semilinear non-autonomous wave equation with distributed delay and analytic nonlinearity
    Feng, Baowei
    NONLINEARITY, 2024, 37 (09)
  • [48] Asymptotic behavior of solutions for a periodic transport equation with delay
    Wuhan Univ J Nat Sci, 2 (135-138):
  • [49] ASYMPTOTIC-BEHAVIOR OF A NONLINEAR DELAY DIFFERENCE EQUATION
    YAN, J
    LIU, B
    APPLIED MATHEMATICS LETTERS, 1995, 8 (06) : 1 - 5
  • [50] Asymptotic Behavior of Solutions for a Periodic Transport Equation with Delay
    Fu Yiping
    WuhanUniversityJournalofNaturalSciences, 1998, (02) : 135 - 138
12345