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A note on stability in three-phase-lag heat conduction

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2008

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Quintanilla, Ramon

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https://doi.org/10.1016/j.ijheatmasstransfer.2007.04.045
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International Journal of Heat and Mass Transfer. Elsevier. 2008, 51(1-2), pp. 24-29. ISSN 0017-9310. eISSN 1879-2189. Available under: doi: 10.1016/j.ijheatmasstransfer.2007.04.045

Zusammenfassung

In this note we consider two cases in the theory of the heat conduction models with three-phase-lag. For each one we propose a suitable Lyapunov function. These functions are relevant tools which allow to study several qualitative properties. We obtain conditions on the material parameters to guarantee the exponential stability of solutions. The spectral analysis complements the results and we show that if the conditions obtained to prove the exponential stability are not satisfied, then we can obtain the instability of solutions for suitable domains. We believe that this kind of results is fundamental to clarify the applicability of the models.

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510 Mathematik

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ISO 690QUINTANILLA, Ramon, Reinhard RACKE, 2008. A note on stability in three-phase-lag heat conduction. In: International Journal of Heat and Mass Transfer. Elsevier. 2008, 51(1-2), pp. 24-29. ISSN 0017-9310. eISSN 1879-2189. Available under: doi: 10.1016/j.ijheatmasstransfer.2007.04.045
BibTex
@article{Quintanilla2008stabi-714.2,
  year={2008},
  doi={10.1016/j.ijheatmasstransfer.2007.04.045},
  title={A note on stability in three-phase-lag heat conduction},
  number={1-2},
  volume={51},
  issn={0017-9310},
  journal={International Journal of Heat and Mass Transfer},
  pages={24--29},
  author={Quintanilla, Ramon and Racke, Reinhard}
}
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