Bresse-Timoshenko type systems with thermodiffusion effects: well-possedness, stability and numerical results

Elhindi, Mohammad; Zennir, Khaled; Ouchenane, Djamel; Choucha, Abdelbaki; Arwadi, Toufic El

doi:10.1007/s12215-021-00672-0

Cited by 11 publications

(10 citation statements)

References 21 publications

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“…In this section, we present the numerical scheme based on P 1 -…nite element approximation for space discretization and implicit Euler scheme for time discretization, we show some numerical examples to demonstrate the decay of the discrete energy and the behavior of the solutions (see [15] , [16] ).…”

Section: Numerical Resultsmentioning

confidence: 99%

On the stability of Lord Shulman thermoelastic system with porous damping

Boudeliou

Bouraoui

Djebabla

2022

Preprint

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In this work, we study the asymptotic behavior of a one-dimensional Lord-Shulman thermoelastic system [1]. We establish the well-posedness and the stability of the system by using the energy method. We present a finite element approximation and we show the discrete energy decay. At the end, numerical simulations are presented to validate the theoretical results.AMS Subject Classification: 435B37, 35L55, 74D05, 93D15.

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Section: Numerical Resultsmentioning

confidence: 99%

On the stability of Lord Shulman thermoelastic system with porous damping

Boudeliou

Bouraoui

Djebabla

2022

Preprint

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“…For more results on the numerical study of the Bresse systems, we refer the reader to previous works. [18][19][20][21][22]…”

Section: Literature Overviewmentioning

confidence: 99%

“…They introduced a fully discrete approximations based on the finite difference method element in time and space and showed the numerical exponential decay for system as well as same the numerical computations. For more results on the numerical study of the Bresse systems, we refer the reader to previous works 18–22 …”

Section: Literature Overviewmentioning

confidence: 99%

Exponential stability for a thermoelastic Bresse system: Theoretical and numerical study

Bouraoui

Djebabla

Arwadi

et al. 2022

Math Methods in App Sciences

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This study aims to investigate numerically and theoretically a thermoelastic Bresse system where the heat conduction given by the Green and Naghdi theories. Theoretically, we establish the existence and uniqueness of solutions as well as the exponential stability regardless of the system's parameters. Numerically, we present a finite element approximation, and we show the discrete energy decay. At the end, we provide some numerical results with an error estimate based on additional regularity of the solution.

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“…The number of research works dealing with thermoelastic problems is huge (see, e.g., Refs. [5, 6‐8, 9, 10]). This paper considers the thermoelastic porous system under the action of dual‐phase‐lag theory the effect of phase lag on the vibration of the Timoshenko beam was studied by Kumar in 11 .…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of the porous elastic system with dual phase lag model: Classical versus second spectrum perspectives

2023

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This paper aims to analyze the energy decay of the thermoelastic porous system. The dual‐phase lag theory is used to model heat transfer. We consider two perspectives: the classical approach and the second spectrum approach. For the classical approach, the well‐posedness is obtained via the semigroup theory and the system is exponentially stable under equal wave speed conditions. On the opposite, we show a polynomial decay. On the other hand, the well‐posedness of the truncated system is obtained via the Faedo Galerkin method, and the system is exponentially stable without any assumptions on the physical parameters.

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Bresse-Timoshenko type systems with thermodiffusion effects: well-possedness, stability and numerical results

Cited by 11 publications

References 21 publications

On the stability of Lord Shulman thermoelastic system with porous damping

On the stability of Lord Shulman thermoelastic system with porous damping

Exponential stability for a thermoelastic Bresse system: Theoretical and numerical study

Asymptotic behavior of the porous elastic system with dual phase lag model: Classical versus second spectrum perspectives

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