Exponential stability and numerical simulation of a Bresse-Timoshenko system subject to a neutral delay

Houssem Eddine Khochemane; Ali Rezaiguia; Hasan Nihal Zaidi; Houssem Eddine Khochemane; Ali Rezaiguia; Hasan Nihal Zaidi

doi:10.3934/math.20231038

AIMS Mathematics

2023, Volume 8, Issue 9: 20361-20379. doi: 10.3934/math.20231038

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Research article

Exponential stability and numerical simulation of a Bresse-Timoshenko system subject to a neutral delay

1.
Higher Normal School of Technological Education of Skikda, Algeria
2.
Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
3.
Department of Computer Science and Mathematics, Mouhamed Cherif Messadia University, Souk Ahras, Algeria

Received: 02 May 2023 Revised: 08 June 2023 Accepted: 11 June 2023 Published: 21 June 2023
MSC : 35B40, 35L70, 93D20

In the present work, we consider a one-dimensional Bresse-Timoshenko system with neutral delay term and a viscous damping acting on vertical displacement of the beam. Under appropriate assumptions on the kernel of this kind of delay and based on the multipliers method, we construct a suitable Lyapunov functional that allows us to establish an exponential decay of the energy in spite of the existence of the delay. Moreover, our result does not depend on any condition on the coefficients of the system. Finally, we present some numerical results to illustrate the theoretical result obtained.
- Bresse-Timoshenko system,
- neutral delay,
- exponential stability,
- energy method,
- Lyapunov functional
Citation: Houssem Eddine Khochemane, Ali Rezaiguia, Hasan Nihal Zaidi. Exponential stability and numerical simulation of a Bresse-Timoshenko system subject to a neutral delay[J]. AIMS Mathematics, 2023, 8(9): 20361-20379. doi: 10.3934/math.20231038

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Abstract

In the present work, we consider a one-dimensional Bresse-Timoshenko system with neutral delay term and a viscous damping acting on vertical displacement of the beam. Under appropriate assumptions on the kernel of this kind of delay and based on the multipliers method, we construct a suitable Lyapunov functional that allows us to establish an exponential decay of the energy in spite of the existence of the delay. Moreover, our result does not depend on any condition on the coefficients of the system. Finally, we present some numerical results to illustrate the theoretical result obtained.

References

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