ON THE ASYMPTOTIC STABILITY OF A BRESSE SYSTEM WITH TWO FRACTIONAL DAMPING TERMS: THEORETICAL AND NUMERICAL ANALYSIS

被引：11
作者：
Bentrcia, Toufik [1 ]
Mennouni, Abdelaziz [1 ]
机构：
[1] Univ Batna 2 Mostefa Benboulaid, Fac Math & Comp Sci, Dept Math, Lab Math Tech LTM, Batna 05078, Algeria
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2023年 / 28卷 / 01期
关键词：
Bresse system; fractional damping; asymptotic stability; finite differ-ence scheme; convergence; DECAY-RATE; ENERGY DECAY; EQUATION; RATES;
D O I：
10.3934/dcdsb.2022090
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this work is to investigate the asymptotic stability of a viscoelastic Bresse system in one dimensional bounded domain. In this context, we introduce two internal damping terms expressed using the generalized Caputo fractional derivative. By adopting a diffusive representation, we show the well-posedness of the proposed system and we prove some decay results. In order to validate the theoretical findings, we implement a finite difference method and we conduct intensive numerical simulations. Moreover, we provide some insights on the convergence of the elaborated numerical scheme.
引用
收藏
页码：580 / 622
页数：43
相关论文
共 50 条
  • [31] Existence and global asymptotic stability in a fractional double parabolic chemotaxis system with logistic source
    Lei, Yuzhu
    Liu, Zuhan
    Zhou, Ling
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 217
  • [32] Asymptotic stability and fold bifurcation analysis in Caputo-Hadamard type fractional differential system
    Ma, Li
    Huang, Ruoyan
    CHINESE JOURNAL OF PHYSICS, 2024, 88 : 171 - 197
  • [33] Theoretical and numerical stability results for a viscoelastic swelling porous-elastic system with past history
    Al-Mahdi, Adel M.
    Al-Gharabli, Mohammad M.
    Alahyane, Mohamed
    AIMS MATHEMATICS, 2021, 6 (11): : 11921 - 11949
  • [34] Global existence and asymptotic stability for coupled nonlinear Klein-Gordon equations with nonlinear damping terms
    Ye, Yaojun
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2013, 28 (02): : 287 - 298
  • [35] Asymptotic stability and blow-up for the wave equation with degenerate nonlocal nonlinear damping and source terms
    Zhang, Hongwei
    Li, Donghao
    Zhang, Wenxiu
    Hu, Qingying
    APPLICABLE ANALYSIS, 2022, 101 (09) : 3170 - 3181
  • [36] On the asymptotic stability of the time-fractional Lengyel-Epstein system
    Mansouri, Djamel
    Abdelmalek, Salem
    Bendoukha, Samir
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 78 (05) : 1415 - 1430
  • [37] Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation
    Zahariev, Andrey
    Kiskinov, Hristo
    MATHEMATICS, 2020, 8 (03)
  • [38] On the asymptotic stability of linear system of fractional-order difference equations
    Abu-Saris, Raghib
    Al-Mdallal, Qasem
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2013, 16 (03) : 613 - 629
  • [39] Asymptotic Behavior of Solutions in Nonlinear Neutral System with Two Volterra Terms
    Mesmouli, Mouataz Billah
    Ardjouni, Abdelouaheb
    Saber, Hicham
    MATHEMATICS, 2023, 11 (12)
  • [40] On the asymptotic stability of linear system of fractional-order difference equations
    Raghib Abu-Saris
    Qasem Al-Mdallal
    Fractional Calculus and Applied Analysis, 2013, 16 : 613 - 629
12345