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Well-posedness and decay property for the Cauchy problem of the standard linear solid model with thermoelasticity of type III

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Abstract

In this paper, we investigate the Cauchy problem related to the standard linear solid model with thermoelasticity of type III in the whole space. By using semigroup theory, we first establish the well-posedness result under certain assumptions on the parameters. By applying the energy method in the Fourier space, we then prove the optimal decay estimate results for both the non-critical and critical cases. Specifically, the decay property of the system is not of the regularity-loss type. In addition, we study the asymptotic expansion of the eigenvalues to analyze the optimality of the decay results.

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Funding

This work was supported by the 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

    Danhua Wang, Wenjun Liu & Kewang Chen

  2. Center for Applied Mathematics of Jiangsu Province, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Wenjun Liu & Kewang Chen

  3. Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Wenjun Liu & Kewang Chen

  4. College of Information Engineering, Nanjing Xiaozhuang University, Nanjing, 211171, China

    Danhua Wang

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  1. Danhua Wang
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  2. Wenjun Liu
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Correspondence to Wenjun Liu.

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Wang, D., Liu, W. & Chen, K. Well-posedness and decay property for the Cauchy problem of the standard linear solid model with thermoelasticity of type III. Z. Angew. Math. Phys. 74, 70 (2023). https://doi.org/10.1007/s00033-023-01964-4

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  • DOI: https://doi.org/10.1007/s00033-023-01964-4

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