Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 9
97
Views
1
CrossRef citations to date
0
Altmetric
Articles

General decay for a nonlinear Bresse system with memory conditions on part of the boundary

, &
Pages 1949-1971 | Received 11 Jun 2019, Accepted 16 Sep 2019, Published online: 03 Oct 2019

References

  • Khemmoudj A, Hamadouche T. General decay of solutions of a Bresse system with viscoelastic boundary conditions. Discrete Contin Dyn Syst. 2017;37(9):4857–4876.
  • Bresse JAC. Cours mécanique Appliquée. Paris: Mallet Bachelier; 1859.
  • Lagnese JE, Leugering G, Schmidt EJPG. Modeling, analysis and control of dynamic elastic multi-link structures. Systems & control: foundations & applications. Boston (MA): Birkhäuser Boston, Inc.; 1994.
  • Alabau Boussouira F, Muñoz Rivera JE, Almeida Júnior DS. Stability to weak dissipative Bresse system. J Math Anal Appl. 2011;374(2):481–498.
  • Fatori LH, Monteiro RN. The optimal decay rate for a weak dissipative Bresse system. Appl Math Lett. 2012;25(3):600–604.
  • Guesmia A, Kafini M. Bresse system with infinite memories. Math Methods Appl Sci. 2015;38(11):2389–2402.
  • Khemmoudj A, Hamadouche T. Boundary stabilization of a Bresse-type system. Math Methods Appl Sci. 2016;39(12):3282–3293.
  • Liu Z, Rao B. Energy decay rate of the thermoelastic Bresse system. Z Angew Math Phys. 2009;60(1):54–69.
  • Noun N, Wehbe A. Stabilisation faible interne locale de système élastique de Bresse. C R Math Acad Sci Paris. 2012;350(9-10):493–498.
  • Qin Y, Yang X-G, Ma Z. Global existence of solutions for the thermoelastic Bresse system. Commun Pure Appl Anal. 2014;13(4):1395–1406.
  • Soriano JA, Muñoz Rivera JE, Fatori LH. Bresse system with indefinite damping. J Math Anal Appl. 2012;387(1):284–290.
  • Santos ML, Soufyane A, Almeida Júnior DS. Asymptotic behavior to Bresse system with past history. Quart Appl Math. 2015;73(1):23–54.
  • Feng BW. General decay rates for a viscoelastic wave equation with dynamic boundary conditions and past history, Art. 103. Mediterr J Math. 2018;15(3):1–17.
  • Feng B, Liu G. Well-posedness and stability of two classes of plate equations with memory and strong time-dependent delay. Taiwanese J Math. 2019;23(1):159–192.
  • Guesmia A, Messaoudi SA. General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping. Math Methods Appl Sci. 2009;32(16):2102–2122.
  • Liu WJ. Arbitrary rate of decay for a viscoelastic equation with acoustic boundary conditions. Appl Math Lett. 2014;38:155–161.
  • Liu WJ, Chen KW. Existence and general decay for nondissipative distributed systems with boundary frictional and memory dampings and acoustic boundary conditions. Z Angew Math Phys. 2015;66(4):1595–1614.
  • Liu WJ, Sun Y, Li G. On decay and blow-up of solutions for a singular nonlocal viscoelastic problem with a nonlinear source term. Topol Methods Nonlinear Anal. 2017;49(1):299–323.
  • Liu WJ, Sun Y. General decay of solutions for a weak viscoelastic equation with acoustic boundary conditions. Z Angew Math Phys. 2014;65(1):125–134.
  • Liu WJ, Yu J. On decay and blow-up of the solution for a viscoelastic wave equation with boundary damping and source terms. Nonlinear Anal. 2011;74(6):2175–2190.
  • Messaoudi SA. General decay of solution of a viscoelastic equation. J Math Anal Appl. 2008;341(2):1457–1467.
  • Park SH. General decay of a transmission problem for kirchhoff type wave equations with boundary memory condition. Acta Math Sci Ser B Engl Ed. 2014;34(5):1395–1403.
  • Park JY, Park SH. Decay rate estimates for wave equations of memory type with acoustic boundary conditions. Nonlinear Anal. 2011;74(3):993–998.
  • Qin YM, Feng BW, Zhang M. Uniform attractors for a non-autonomous viscoelastic equation with a past history. Nonlinear Anal. 2014;101:1–15.
  • Tahamtani F, Peyravi A. Asymptotic behavior and blow-up of solutions for a nonlinear viscoelastic wave equation with boundary dissipation. Taiwanese J Math. 2013;17(6):1921–1943.
  • Cavalcanti MM, Guesmia A. General decay rates of solution to a nonlinear wave equation with boundary condition of memory type. Differ Integral Equ. 2005;18(5):583–600.
  • Messaoudi SA, Soufyane A. General decay of solution of a wave equation with a boundary control of memory type. Nonlinear Anal Real World Appl. 2010;11(4):2896–2904.
  • Shin S-Y, Kang J-R. General decay for the degenerate equation with a memory condition at the boundary. Abstr Appl Anal. 2013;2013:1–8.
  • Mustafa MI, Abusharkh GA. Plate equations with viscoelastic boundary damping. Indag Math (NS). 2015;26(2):307–323.
  • Boulanouar F, Drabla S. General boundary stabilization result of memory-type thermoelasticity with second sound. Electron J Diff Equ. 2014;2014(202):1–18.
  • Chen KW, Liu WJ, Yu J. Existence and general decay of a transmission problem for the plate equation with a memory condition on the boundary, Art. 12. Z Angew Math Phys. 2016;67(1):1–39.
  • Mustafa MI. Boundary stabilization of memory-type thermoelasticity with second sound. Z Angew Math Phys. 2012;63(4):777–792.
  • Munoz Rivera JE, Racke R. Magneto-thermo-elasticity – large-time behavior for linear systems. Adv Differ Equ. 2001;6(3):359–384.
  • Pei P, Rammaha MA, Toundykov D. Local and global well-posedness of semilinear Reissner-Mindlin-Timoshenko plate equations. Nonlinear Anal. 2014;105:62–85.
  • Arnold VI. Mathematical methods of classical mechanics. Translated from the Russian by K. Vogtmann and A. Weinstein, 2nd ed. Graduate Texts in Mathematics, 60. New York: Springer; 1989.

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.