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Well-posedness and exponential stability of a coupled fluid–thermoelastic plate interaction model with second sound

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Abstract

In this paper, we investigate a coupled system modeled by fluid and thermoelastic plate, while the heat effects are modeled by the Cattaneo’s law giving rise to a “second sound” effect. We proved that the coupled system admits a unique global mild solution. Furthermore, we construct the second-order energy to control the term \( \Vert \nabla \theta \Vert _{L^2(\Gamma _0)} \) so as to establish the exponential decay of the solutions.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 12271261), the Key Research and Development Program of Jiangsu Province (Social Development) (No. BE2019725) and the Qing Lan Project of Jiangsu Province.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Jian Jiang & Wenjun Liu

  2. Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Center for Applied Mathematics of Jiangsu Province, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Wenjun Liu

  3. College of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Jian Jiang

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  1. Jian Jiang
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J. J. and W. L. wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Wenjun Liu.

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Jiang, J., Liu, W. Well-posedness and exponential stability of a coupled fluid–thermoelastic plate interaction model with second sound. Z. Angew. Math. Phys. 74, 132 (2023). https://doi.org/10.1007/s00033-023-02025-6

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  • DOI: https://doi.org/10.1007/s00033-023-02025-6

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