Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 16
107
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Uniform dynamics of partially damped semilinear Bresse systems

ORCID Icon, ORCID Icon, & ORCID Icon
Pages 4548-4562 | Received 02 Jun 2021, Accepted 02 Sep 2022, Published online: 19 Sep 2022

References

  • Bresse JAC. Cours de Méchanique appliquée. Paris: Mallet Bachelier; 1859.
  • Lagnese JE, Leugering G, G. Schmidt EJP. Modeling, analysis and control of dynamic elastic multi-link structures. Boston: Birkhaüser; 1994.
  • Soufyane A, Said-Houari B. The effect of the wave speeds and the frictional damping terms on the decay rate of the Bresse system. Evol Equ Control Theory. 2014;3:713–738.
  • Soufyane A. Stabilisation de la poutre de Timoshenko. C R Acad Sci Paris Sér I Math. 1999;328(8):731–734.
  • Timoshenko S. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philos Mag. 1921;41:744–746.
  • Liu Z, Rao B. Energy decay rate of the thermoelastic Bresse system. Z Angew Math Phys. 2009;60:54–69.
  • Alabau Boussouira F, Muñoz Rivera JE, Almeida Júnior DS. Stability to weak dissipative Bresse system. J Math Anal Appl. 2011;374:481–498.
  • Araújo RO, Marinho SS, Prates Filho JS. Uniform stability of a non-autonomous semilinear Bresse system with memory, Appl Math Comput 387 (2020), article 124418, 11 pp.
  • Bittencourt Moraes GE, Jorge Silva MA. Arched beams of Bresse type: observability and application in thermoelasticity. Nonlinear Dynam. 2021;103:2365–2390.
  • Dell'Oro F. Asymptotic stability of thermoelastic systems of Bresse type. J Differ Equ. 2015;258:3902–3927.
  • Fatori LH, Muñoz Rivera JE. Rates of decay to weak thermoelastic Bresse system. IMA J Appl Math. 2010;75:881–904.
  • Muñoz Rivera JE, Naso MG. Boundary stabilization of Bresse systems, Z Angew Math Phys. 70 (2019), article 56, 16 pp.
  • Said-Houari B, Hamadouche T. The asymptotic behavior of the Bresse–Cattaneo system, Commun Contemp Math 18 (2016), article 1550045, 18 pp.
  • Wehbe A, Youssef W. Exponential and polynomial stability of an elastic Bresse system with two locally distributed feedbacks, J Math Phys 51 (2010), article 103523, 17 pp.
  • Alves MS, Jorge Silva MA, Ma TF, et al. Non-homogeneous thermoelastic Timoshenko systems. Bull Braz Math Soc. 2017;48:461–484.
  • Ammar-Khodja F, Benabdallah A, Muñoz Rivera JE, et al. Energy decay for Timoshenko systems of memory type. J Differ Equ. 2003;194:82–115.
  • Ma TF, Monteiro RN. Singular limit and long-time dynamics of Bresse systems. SIAM J Math Anal. 2017;49:2468–2495.
  • Chueshov I. Dynamics of quasi-stable dissipative systems, universitext. Cham: Springer; 2015.
  • Chueshov I, Lasiecka I. Von karman evolution equations. well-posedness and long-time dynamics, springer monographs in mathematics. New York: Springer; 2010.
  • Fatori LH, Alves MO, Fernández Sare HD. Stability conditions to Bresse systems with indefinite memory dissipation. Appl Anal. 2018;99:1066–1084.
  • Guesmia A. Non-exponential and polynomial stability results of a Bresse system with one infinite memory in the vertical displacement. Nonauton Dyn Syst. 2017;4:78–97.
  • Messaoudi SA, Hassan JH. New general decay results in a finite-memory Bresse system. Commun Pure Appl Anal. 2019;18:1637–1662.
  • Guesmia A, Kirane M. Uniform and weak stability of Bresse system with two infinite memories, Z Angew Math Phys 67 (2016), article 124, 39 pp.
  • Hale JK. Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., vol. 25, American Mathematical Society, Providence, 1988.
  • Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci. Vol. 68, Springer-Verlag, New York, 1988.
  • Fatori LH, Jorge Silva MA, Narciso V. Quasi-stability property and attractors for a semilinear Timoshenko system. Discrete Contin Dyn Syst. 2016;36:6117–6132.
  • Miranville A, Zelik S. Handbook of Differential Equations, Evolutionary Equations, Volume 4, Chapter 3, C. M. Dafermos and M. Pokorny, Editors, Elsevier, 2008.

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.