Issues related to the second spectrum, Ostrogradsky’s energy and the stabilization of Timoshenko–Ehrenfest-type systems

Júnior, D. S. Almeida; Ramos, A. J. A.; Soufyane, Abdelaziz; Cardoso, M. L.; Santos, M. L.

doi:10.1007/s00707-020-02730-7

Cited by 11 publications

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“…They further show that for any values of the system's coefficients, dissipative Timoshenko‐type systems free of the second spectrum are exponentially stable, based on crucial scientific and historical discoveries by Elishakoff. For more results about the stability of the Bresse‐Timoshenko type systems see the following articles 18,19–21 …”

Section: Introductionmentioning

confidence: 99%

“…They further show that for any values of the system's coefficients, dissipative Timoshenko-type systems free of the second spectrum are exponentially stable, based on crucial scientific and historical discoveries by Elishakoff. For more results about the stability of the Bresse-Timoshenko type systems see the following articles. 18,[19][20][21] The rest of this paper is as follows: In Section 2, we study the well-posedness of the onedimensional porous materials with microtemperature. In Section 3, we establish the exponential decay under the conditions on the one-dimensional porous materials with microtemperature parameters.…”

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confidence: 99%

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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%

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confidence: 99%