STABILITY OF A TIMOSHENKO SYSTEM
WITH CONSTANT DELAY
Innocent Ouedraogo1, Gilbert Bayili2
1,2 Department of Mathematics
Joseph KI-ZERBO University
03 BP 7021 Ouagadougou, BURKINA FASO

Abstract

The aim of this work is to develop a detail analysis of a Timoshenko type beam model taking into account a delay. We prove the well-posedness and regularity of solution, explained using the theory of the Faedo-Galerkin scheme. Namely, under a suitable choice of Lyapunov functional, exponential decay of the whole energy holds.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 2
Year: 2023

DOI: 10.12732/ijam.v36i2.6

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] J.D.S. Almeida, A.R.J.A. Anderson and M.M. Freitas, Energy decay for damped Shear beam model and new facts related to the classical Timoshenko system, Applied Mathematics Letters, 120 (2021), 107324.
  2. [2] G. Bayili, S. Nicaise and R. Silga, Rational energy decay rate for the wave equation with delay term on the dynamical control, Journal of Mathematical Analysis and Applications, 495, No 1 (2021), 124693.
  3. [3] S. Chen, JW. Hinson, J. Lee, David Harry Miller,V. Pavlunin, EI Shibata, IPJ Shipsey, D. Cronin-Hennessy, Adam L. Lyon, EH Thorndike, and others, Branching fraction and photon energy spectrum for , Physical Review Letters, 87, No 25 (2001), 251807.
  4. [4] M. Chen, W. Liu and W. Zhou, Existence and general stabilization of the Timoshenko system of thermo-viscoelasticity of type III with frictional damping and delay terms, Advances in Nonlinear Analysis, 7, No 4 (2018), 547-569.
  5. [5] D.B. Claude, Feedback stabilizability in Hilbert spaces, Applied Mathematics and Optimization, 4, No 1 (1977), 225-248.
  6. [6] S. Djebali, Youcef BELGAID Les injections compactes, th´eorie et applications (2015).
  7. [7] A. Moussa, Some variants of the classical Aubin–Lions lemma, Journal of Evolution Equations, 16, No 1 (2016), 65-93.
  8. [8] S. Nicaise and C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM Journal on Control and Optimization, 45, No 5 (2006), 1561-1585.
  9. [9] S. Parrott, On a quotient norm and the Sz.-Nagy-Foia¸s lifting theorem, Journal of Functional Analysis, 30, No 3 (1978), 311-328.
  10. [10] F. Yazid, Global existence and stability for some hyperbolic systems (2020).