Asymptotic behavior of Timoshenko beams with delayed viscoelasticity acting on the shear force

被引：0
作者：
A. J. A. Ramos
C. A. Nonato
C. A. Raposo
M. M. Freitas
M. L. Araújo
机构：
[1] Federal University of Pará,Faculty of Mathematics
[2] Ceará State University,Mathematics Department
[3] Federal University of Bahia,Mathematics Department
来源：
Zeitschrift für angewandte Mathematik und Physik | 2023年 / 74卷
关键词：
Timoshenko system; Well-posedness; Delayed viscoelasticity; Polynomial decay; Primary 35A01; Secondary 35A02; 35B35;
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摘要：
In this work, we use the theory of semigroups to study the well-posedness and the asymptotic behavior of the Timoshenko beam system with delayed viscoelastic damping acting only on the shear force. This system is different from all others related to time delay terms. We use the Lumer–Phillips theorem to prove the well-posedness of the problem and then use the contrapositive of the Gearhart–Prüss–Huang theorem to prove the lack of exponential decay independent of any relationship between the velocities. Finally, we use the Borichev–Tomilov theorem for optimal rate polynomial decay.
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  • [1] Borichev A(2010)Optimal polynomial decay of functions and operator semigroups Math. Ann. 347 455-478
  • [2] Tomilov Y(2022)Optimal stability results for laminated beams with Kelvin-Voigt damping and delay J. Math. Anal. Appl. 514 126328-156
  • [3] Cabanillas Zannini VR(1986)An example on the effect of time delays in boundary feedback stabilization of wave equations SIAM J. Control. Optim. 24 152-6850
  • [4] Potenciano-Machado L(1978)Spectral theory for contraction semigroups on Hilbert space Trans. Amer. Math. Soc. 236 1088-1264
  • [5] Quispe Méndez T(2001)Cargo pendulation reduction on ship-nounted cranes via Boom-Luff angle actuation J. Vib. Control 7 1253-56
  • [6] Datko R(1985)Characteristic condition for exponential stability of linear dynamical systems in Hilbert space Ann. Differ. Equ. 1 43-2964
  • [7] Lagnese J(2021)Exponential decay and well-posedness for a one-dimensional porous-elastic system with distributed delay Appl. Anal. 100 2950-503
  • [8] Polis MP(2020)Stability result for a nonlinear damping porous-elastic system with delay term Nonlinear Stud. 27 487-6317
  • [9] Gearhart L(2021)Optimal polynomial decay for a Timoshenko system with a strong damping and a strong delay Math. Meth. Appl. Sci. 44 6301-277
  • [10] Henry RJ(2003)Delayed position-feedback controller for the reduction of payload pendulations of rotary cranes J. Vib. Control 9 257-1585
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