On the stability of Bresse system with one discontinuous local internal Kelvin–Voigt damping on the axial force

被引:0
作者
Mohammad Akil
Haidar Badawi
Serge Nicaise
Ali Wehbe
机构
[1] Université Savoie Mont Blanc,Faculty of Sciences 1, Khawarizmi Laboratory of Mathematics and Applications
[2] LAMA,KALMA
[3] Université Polytechnique Hauts-de-France,undefined
[4] LAMAV,undefined
[5] Lebanese University,undefined
来源
Zeitschrift für angewandte Mathematik und Physik | 2021年 / 72卷
关键词
Bresse system; Kelvin–Voigt damping; Strong stability; Polynomial stability; Frequency domain approach; 93D15; 93D20; 35L05; 93C80; 74K10; 35Q74; 35B40; 35B35;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper, we investigate the stabilization of a linear Bresse system with one discontinuous local internal viscoelastic damping of Kelvin–Voigt type acting on the axial force, under fully Dirichlet boundary conditions. First, using a general criteria of Arendt–Batty, we prove the strong stability of our system. Finally, using a frequency domain approach combined with the multiplier method, we prove that the energy of our system decays polynomially with different rates.
引用
收藏
相关论文
共 85 条
  • [1] Abdallah F(2018)Stability results of a distributed problem involving Bresse system with history and/or Cattaneo law under fully Dirichlet or mixed boundary conditions Math. Methods Appl. Sci. 41 1876-1907
  • [2] Ghader M(2020)On the exponential and polynomial stability for a linear Bresse system Math. Methods Appl. Sci. 43 2626-2645
  • [3] Wehbe A(2020)Stability and exact controllability of a Timoshenko system with only one fractional damping on the boundary Asymptot. Anal. 119 3-4
  • [4] Afilal M(2011)Stability to weak dissipative Bresse system J. Math. Anal. Appl. 374 481-498
  • [5] Guesmia A(2014)The lack of exponential stability in certain transmission problems with localized Kelvin–Voigt dissipation SIAM J. Appl. Math. 74 345-365
  • [6] Soufyane A(2013)The asymptotic behavior of the linear transmission problem in viscoelasticity Math. Nachr. 287 483-497
  • [7] Zahri M(1988)Tauberian theorems and stability of one-parameter semigroups Trans. Am. Math. Soc. 306 837-852
  • [8] Akil M(2015)Polynomial stability of the Timoshenko system by one boundary damping J. Math. Anal. Appl. 425 1177-1203
  • [9] Chitour Y(2016)Stability results of some distributed systems involving mindlin-Timoshenko plates in the plane ZAMM J. Appl. Math. Mech. 96 916-938
  • [10] Ghader M(2008)Non-uniform stability for bounded semi-groups on Banach spaces J. Evol. Equ. 8 765-780