Well-posedness and general decay for a porous-elastic system with microtemperatures effects and time-varying delay term

Foughali, Fouzia; Zitouni, Salah; Bouzettouta, Lamine; Khochemane, Houssem Eddine

doi:10.1007/s00033-022-01801-0

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…Then they demonstrated the plynomial decay and optimality. For comprehensive insights, refer to references [5,7,12,13,16]. Inspiriting by previous work, in our article, we study the Timoshenko system below with a strong damping and a strong distributed delay when it acts on the first equation:…”

Section: Introductionmentioning

confidence: 97%

Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Laribi,

Krelifa,

Zitouni

et al. 2023

Preprint

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In this research work, we study the linear Timoshenko problem with a strong damping and a strong distributed delay when it acts on the first equation. We first prove the existence and uniqueness solution of the system by using the semi-group theory. Then, we illustrate the lack of exponential stability even in the condition of equal wave propagation is satisfied. Furthermore, we show the polynomial decay of solution with rate t−½. From this perspective, we demonstrate the optimality of the rate.

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Section: Introductionmentioning

confidence: 97%

Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Laribi,

Krelifa,

Zitouni

et al. 2023

Preprint

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“…Te importance of the microtemperature appears in many works and this is due to the fact that many phenomena are afected by the heat present in the microvolume of bodies which is known as the microtemperature. Furthermore, the asymptotic behavior of solutions for the diferent types of problems is under the great infuence of the microtemperature efect cited in [14][15][16][17][18][19][20][21][22][23][24] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, from equation (20), we obtain equation (52). Now, we can state and prove the following stability result.…”

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confidence: 99%

Exponential Decay of Swelling Porous Elastic Soils with Microtemperatures Effects

Rezaiguia

Zitouni

Zaidi

2023

Journal of Mathematics

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In this article, we considered the one-dimensional swelling problem in porous elastic soils with microtemperatures effects in the case of fluid saturation. First, we showed that the system is well-posed in the sens of semigroup. Then, we constructed a suitable Lyapunov functional based on the energy method and we proved that the dissipation given only by the microtemperatures is strong enough to provoke an exponential stability for the solution irrespective of the wave speeds of the system.

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Well-posedness and general decay for a porous-elastic system with microtemperatures effects and time-varying delay term

Cited by 2 publications

References 17 publications

Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Polynomial stability of Timoshenko system with strong damping and strong distributed delay terms

Exponential Decay of Swelling Porous Elastic Soils with Microtemperatures Effects

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