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

Bouraoui, Hamed Abderrahmane; Djebabla, Abdelhak; Arwadi, Toufic El; Haiour, Mohamed

doi:10.1002/mma.8885

Cited by 3 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We introduce a discretization by finite elements in space and backward Euler scheme in time (see Reference 25).…”

Section: The Discrete Problemmentioning

confidence: 99%

Exponential stability and numerical analysis of Timoshenko system with dual‐phase‐lag thermoelasticity

Bouraoui,

Djebabla,

Sahari

et al. 2023

Int J Numerical Modelling

Self Cite

View full text Add to dashboard Cite

This study aims to investigate the well‐posedness and stability of a thermoelastic Timoshenko system with non‐Fourier heat conduction. Specifically, we analyze the system using the dual‐phase‐lag (DPL) model, which incorporates two thermal relaxation times, and , to model non‐instantaneous heat propagation. Applying the semigroup approach, we demonstrate the existence and uniqueness of the solutions. Subsequently, we introduce a novel stability parameter using the multiplier method. Exponential decay is proven for the case of with . Using Gearhart–Prüss theorem, we show the lack of exponential stability when and . Numerically, we present a fully discrete approximation using the finite element method and the backward Euler scheme, and we provide some numerical simulations to show the discrete energy decay and the behavior of solutions.

show abstract

“…We introduce a discretization by finite elements in space and backward Euler scheme in time (see Reference 25).…”

Section: The Discrete Problemmentioning

confidence: 99%

Exponential stability and numerical analysis of Timoshenko system with dual‐phase‐lag thermoelasticity

Bouraoui,

Djebabla,

Sahari

et al. 2023

Int J Numerical Modelling

Self Cite

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach

Zougheib,

El Arwadi

2024

Results in Applied Mathematics

View full text Add to dashboard Cite

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

Cited by 3 publications

References 34 publications

Exponential stability and numerical analysis of Timoshenko system with dual‐phase‐lag thermoelasticity

Exponential stability and numerical analysis of Timoshenko system with dual‐phase‐lag thermoelasticity

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

Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach

Contact Info

Product

Resources

About