Research Article

Exponential decay of thermo-elastic Bresse system with distributed delay term

Volume: 47 Number: 5 October 16, 2018
  • S. Zitouni *
  • L. Bouzettouta
  • Kh. Zennir
  • D. Ouchenane
EN

Exponential decay of thermo-elastic Bresse system with distributed delay term

Abstract

The paper considered here is one-dimensional linear thermo-elastic Bresse system with a distributed delay term in the first equation. We prove the well-posedness and exponential stability result, this later will be shown without the usual assumption on the wave speeds. To achieve our goals, we make use of the semi-group method.

Keywords

References

  1. Alabau-Boussouira, F., Munôz Rivera, J. E., Almeida Junior, D. S., Stability to weak dissipative Bresse system, Journal of Mathematical Analysis and Applications, 374:481-498, 2011.
  2. Benaissa, A., Miloudi, M., Mokhtari, M., Global existence and energy decay of solutions to a Bresse system with delay terms, Comment. Math. Univ. Carolin. 56, 2, 169-186, 2015.
  3. Bouzettouta, L., Zitouni, S., Zennir, Kh., and Guesmia, A., Stability of Bresse system with internal distributed delay, J. Math. Comput. Sci. 7, No. 1, 92-118, 2017.
  4. Bouzettouta, L., Zitouni, S., Zennir, Kh., and Sissaoui, H., Well-posedness and decay of solutions to Bresse system with internal distributed delay, Int. J. Appl. Math. Stat. 56, 4, 1-12, 2017.
  5. Bresse, J. A. C., Cours de Méchanique Appliquée, Mallet Bachelier, Paris, 1859.
  6. Feng, B. and Yang, Xin-Guang, Long-time dynamics for a nonlinear Timoshenko system with delay, Applicable Analysis (2016) http://dx.doi.org/10.1080/00036811.2016.1148139.
  7. Guesmia, A., Asymptotic stability of abstract dissipative systems with infinite memory, J. Math. Anal. Appl. 382 :748-760, 2011.
  8. Guesmia, A. and Kafini, M., Bresse system with infinite memories, Math. Meth. Appl. 2014, DOI: 10.1002/mma.3228.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

S. Zitouni * This is me
Algeria

L. Bouzettouta This is me
Algeria

Kh. Zennir This is me
United Arab Emirates

D. Ouchenane This is me
Algeria

Publication Date

October 16, 2018

Submission Date

May 6, 2017

Acceptance Date

July 10, 2017

Published in Issue

Year 2018 Volume: 47 Number: 5

APA
Zitouni, S., Bouzettouta, L., Zennir, K., & Ouchenane, D. (2018). Exponential decay of thermo-elastic Bresse system with distributed delay term. Hacettepe Journal of Mathematics and Statistics, 47(5), 1216-1230. https://izlik.org/JA64PN57SD
AMA
1.Zitouni S, Bouzettouta L, Zennir K, Ouchenane D. Exponential decay of thermo-elastic Bresse system with distributed delay term. Hacettepe Journal of Mathematics and Statistics. 2018;47(5):1216-1230. https://izlik.org/JA64PN57SD
Chicago
Zitouni, S., L. Bouzettouta, Kh. Zennir, and D. Ouchenane. 2018. “Exponential Decay of Thermo-Elastic Bresse System With Distributed Delay Term”. Hacettepe Journal of Mathematics and Statistics 47 (5): 1216-30. https://izlik.org/JA64PN57SD.
EndNote
Zitouni S, Bouzettouta L, Zennir K, Ouchenane D (October 1, 2018) Exponential decay of thermo-elastic Bresse system with distributed delay term. Hacettepe Journal of Mathematics and Statistics 47 5 1216–1230.
IEEE
[1]S. Zitouni, L. Bouzettouta, K. Zennir, and D. Ouchenane, “Exponential decay of thermo-elastic Bresse system with distributed delay term”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 5, pp. 1216–1230, Oct. 2018, [Online]. Available: https://izlik.org/JA64PN57SD
ISNAD
Zitouni, S. - Bouzettouta, L. - Zennir, Kh. - Ouchenane, D. “Exponential Decay of Thermo-Elastic Bresse System With Distributed Delay Term”. Hacettepe Journal of Mathematics and Statistics 47/5 (October 1, 2018): 1216-1230. https://izlik.org/JA64PN57SD.
JAMA
1.Zitouni S, Bouzettouta L, Zennir K, Ouchenane D. Exponential decay of thermo-elastic Bresse system with distributed delay term. Hacettepe Journal of Mathematics and Statistics. 2018;47:1216–1230.
MLA
Zitouni, S., et al. “Exponential Decay of Thermo-Elastic Bresse System With Distributed Delay Term”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 5, Oct. 2018, pp. 1216-30, https://izlik.org/JA64PN57SD.
Vancouver
1.S. Zitouni, L. Bouzettouta, Kh. Zennir, D. Ouchenane. Exponential decay of thermo-elastic Bresse system with distributed delay term. Hacettepe Journal of Mathematics and Statistics [Internet]. 2018 Oct. 1;47(5):1216-30. Available from: https://izlik.org/JA64PN57SD