Do equal speed condition and exponential stability relate for the truncated thermoelastic Timoshenko system under Green Naghdi law?

Zougheib, Hamza; Arwadi, Toufic El; Madureira, Rodrigo L. R.; Rincon, Mauro A.

doi:10.1080/01495739.2023.2217233

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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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Section: Introductionmentioning

confidence: 99%