Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 7
Submit an article Journal homepage
63
Views
0
CrossRef citations to date
0
Altmetric
Research Article

New stability result of a partially dissipative viscoelastic Timoshenko system with a wide class of relaxation function

Shadi Al-Omaria Preparatory Year Program - Department of Mathematics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia;b Interdisciplinary Research Center for Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-9263-9754View further author information
ORCID Icon
Pages 2123-2140 | Received 20 Feb 2021, Accepted 10 Dec 2021, Published online: 28 Dec 2021

References

  • Timoshenko SP. Lxvi: on the correction for shear of the differential equation for transverse vibrations of prismatic bars. London Edinbur Dubl Phil Magaz J Sci. 1921;41(245):744–746.
  • Timoshenko SPX. On the transverse vibrations of bars of uniform cross-section. London Edinbur Dubl Phil Magaz J Sci. 1922;43(253):125–131.
  • Kim JU, Renardy Y. Boundary control of the Timoshenko beam. SIAM J Control Optimiz. 1987;25(6):1417–1429.
  • Raposo CA, Ferreira J, Santos M, et al. Exponential stability for the Timoshenko system with two weak dampings. Appl Math Lett. 2005;18(5):535–541.
  • Liu Z, Zheng S. Semigroups associated with dissipative systems; 1999.
  • Júnior DA, Santos M, Rivera JM. Stability to weakly dissipative Timoshenko systems. Math Methods Appl Sci. 2013;36(14):1965–1976.
  • Rivera JEM, Racke R. Mildly dissipative nonlinear Timoshenko systems global existence and exponential stability. J Math Anal Appl. 2002;276(1):248–278.
  • Soufyane A, Whebe A. Uniform stabilization for the timoshenko beam by a locally distributed damping. Electron J Differ Equ (EJDE)[electronic only]. Paper–No. 2003. 2003.
  • Ammar-Khodja F, Benabdallah A, Rivera JM, et al. Energy decay for Timoshenko systems of memory type. J Differ Equ. 2003;194(1):82–115.
  • Guesmia A, Messaoudi SA. On the control of a viscoelastic damped Timoshenko-type system. Appl Math Comput. 2008;206(2):589–597.
  • Messaoudi SA, Mustafa MI. A stability result in a memory-type Timoshenko system. Dyn Syst Appl. 2009;18(3):457.
  • Messaoudi SA, Hassan JH, et al. General and optimal decay in a memory-type Timoshenko system. J Integral Equ Appl. 2018;30(1):117–145.
  • Hassan JH, Messaoudi SA, Zahri M. Existence and new general decay results for a viscoelastic Timoshenko system. Zeitsch Anal Ihre Anwend.. 2020;39(2):185–222.
  • Prüss J. Evolutionary integral equations and applications. Vol. 87. Birkhäuser; 2013.
  • Drozdov AD, Kolmanovskii VB. Stability in viscoelasticity. North-Holland Ser Appl Math Mech. 1994;38:1–600.
  • Alves MO, Tavares EHG, Silva MAJ, et al. On modeling and uniform stability of a partially dissipative viscoelastic Timoshenko system. SIAM J Math Anal. 2019;51(6):4520–4543.
  • Mustafa MI. Optimal decay rates for the viscoelastic wave equation. Math Methods Appl Sci. 2018;41(1):192–204.
  • Lions JL. Quelques méthodes de résolution des problemes aux limites non linéaires; 1969.
  • Jin KP, Liang J, Xiao TJ. Coupled second order evolution equations with fading memory: optimal energy decay rate. J Differ Equ. 2014;257(5):1501–1528.
  • Arnold VI. Mathematical methods of classical mechanics. New York: Springer-Verlag; 1982. (Graduate Texts in Mathematics).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.