Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 3
86
Views
6
CrossRef citations to date
0
Altmetric
Research Article

General decay for a viscoelastic-type Timoshenko system with thermoelasticity of type III

, &
Pages 902-920 | Received 18 Dec 2020, Accepted 05 Aug 2021, Published online: 17 Aug 2021

References

  • Timoshenko SP. LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Lond Edinb Dublin Philos Mag J Sci. 1921;41(245):744–746.
  • Ammar-Khodja F, Benabdallah A, Muñoz Rivera JE, 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.
  • Guesmia A, Messaoudi SA. General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping. Math Meth Appl Sci. 2009;32(16):2102–2122.
  • Kim JU, Renardy Y. Boundary control of the Timoshenko beam. SIAM J Control Optim. 1987;25(6):1417–1429.
  • Muñoz Rivera JE, Fernández Sare HD. Stability of Timoshenko systems with past history. J Math Anal Appl. 2008;339(1):482–502.
  • Raposo CA, Ferreira J, Santos ML, Castro NNO. Exponential stability for the Timoshenko system with two weak dampings. Appl Math Lett. 2005;18(5):535–541.
  • Soufyane A. Stabilisation de la poutre de Timoshenko. C R Acad Sci Paris Sr I Math.. 1999;328(8):731–734.
  • Soufyane A, Whebe A. Uniform stabilization for the Timoshenko beam by a locally distributed damping. Electron J Differ Equ. 2003;2003(29):1–14.
  • Muñoz Rivera JE, Racke R. Mildly dissipative nonlinear Timoshenko systems global existence and exponential stability. J Math Anal Appl. 2002;276(1):248–278.
  • Almeida Júnior DS, Santos ML, et al. Stability to 1-D thermoelastic Timoshenko beam acting on shear force. Z Angew Math Phys. 2014;65(6):1233–1249.
  • Apalara TA. General stability of memory-type thermoelastic Timoshenko beam acting on shear force. Contin Mech Thermodyn. 2018;30(2):291–300.
  • Green AE, Naghdi PM. A re-examination of the basic postulates of thermomechanics. Proc R Soc London A. 1991;432(1885):171–194.
  • Green AE, Naghdi PM. On undamped heat waves in an elastic solid. J Thermal Stresses. 1992;15(2):253–264.
  • Green AE, Naghdi PM. Thermoelasticity without energy dissipation. J Elast. 1993;31(3):189–208.
  • Djebabla A, Tatar N. Exponential stabilization of the Timoshenko system by a thermo-viscoelastic damping. J Dyn Control Syst. 2010;16(2):189–210.
  • Djebabla A, Tatar N. Exponential stabilization of the Timoshenko system by a thermal effect with an oscillating kernel. Math Comput Modell. 2011;54(1-2):301–314.
  • Kafini M, Messaoudi SA, Mustafa MI. Energy decay for hyperbolic thermoelastic systems of memory type. Appl Anal. 2014;93(6):1201–1216.
  • Messaoudi SA, Belkacem S-H. Energy decay in a Timoshenko-type system of thermoelasticity of type III. J Math Anal Appl. 2008;348(1):298–307.
  • Messaoudi SA, Belkacem S-H. Energy decay in a Timoshenko-type system with history in thermoelasticity of type III. Adv Differ Equ. 2009;14(3-4):375–400.
  • Messaoudi SA, Fareh A. Energy decay in a Timoshenko-type system of thermoelasticity of type III with different wave-propagation speeds. Arab J Math. 2013;2(2):199–207.
  • Ghennam K, Djebabla A. Energy decay result in a Timoshenko-type system of thermoelasticity of type III with weak damping. Math Methods Appl Sci. 2018;41(10):3868–3884.
  • Apalara TA, Messaoudi SA, Mustafa MI. Energy decay in thermoelasticity type III with viscoelastic damping and delay term. Electron J Differ Equ. 2012;2012(128):1–15.
  • Kafini M, Messaoudi SA, Mustafa MI, et al. Well-posedness and stability results in a Timoshenko-type system of thermoelasticity of type III with delay. Z Angew Math Phys. 2015;66(4):1499–1517.
  • Messaoudi SA, Apalara TA. General stability result in a memory-type porous thermoelasticity system of type III. Arab J Math Sci. 2014;20(2):213–232.
  • Messaoudi SA, Apalara TA. Asymptotic stability of thermoelasticity type III with delay term and infinite memory. IMA J Math Control Inf. 2015;32(1):75–95.

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:

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:

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.