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Uniqueness theorems about high-order time differential thermoelastic models

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The purpose of the present manuscript is to investigate the well-posedness question for three different stand-alone and self-consistent thermoelastic models derived from the time differential formulation of the dual-phase-lag heat conduction law and characterized by Taylor expansion orders higher than those most commonly considered in literature up to now. The main motivation at the basis of this study is that the interaction among multiple energy carriers progressively gains significance as the observation scales reduce and has, as a direct consequence, the involvement of high-order terms in the time differential dual-phase-lag heat conduction constitutive equation. Considering inhomogeneous and anisotropic linear thermoelastic materials, we are able to prove three uniqueness results through the use of appropriate integral operators and Lagrange identities; the results are proved without any restriction imposed on the delay times other than their positivity.

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Acknowledgements

The results contained in the present paper have been partially presented in the Wascom 2017 International Conference in honour of Prof. Tommaso Ruggeri’s 70th birthday.

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  1. Dipartimento di Ingegneria dell’Informazione ed Elettrica e Matematica Applicata, Università di Salerno, via Giovanni Paolo II n. 132, 84084, Fisciano, SA, Italy

    Vittorio Zampoli

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Zampoli, V. Uniqueness theorems about high-order time differential thermoelastic models. Ricerche mat 67, 929–950 (2018). https://doi.org/10.1007/s11587-018-0351-6

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