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Spectrum and stability analysis for a transmission problem in thermoelasticity with a concentrated mass

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Abstract

In this paper, a transmission problem between elastic and thermoelastic material is considered. Assume that these two materials are connected by a vibrating concentrated mass. By a detailed spectral analysis, the asymptotic expressions of the eigenvalues of the system are obtained, and based on which, the Riesz basis property of the eigenvectors is deduced. It is proved that the total energy of this system cannot achieve exponential decay. However, by the frequency domain method together with some multiplier techniques, the polynomial decay of the system is showed and the optimal decay rate is estimated. Finally, some numerical simulations are given to support the results obtained in this paper.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin University, Tianjin, 300072, China

    Zhong-Jie Han & Gen-Qi Xu

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  1. Zhong-Jie Han
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  2. Gen-Qi Xu
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Correspondence to Zhong-Jie Han.

Additional information

This research is supported by the Natural Science Foundation of China Grants NSFC-61104130, 61174080 and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20110032120074).

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Han, ZJ., Xu, GQ. Spectrum and stability analysis for a transmission problem in thermoelasticity with a concentrated mass. Z. Angew. Math. Phys. 66, 1717–1736 (2015). https://doi.org/10.1007/s00033-015-0504-3

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  • DOI: https://doi.org/10.1007/s00033-015-0504-3

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