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Asymptotic profiles of solutions for regularity-loss-type generalized thermoelastic plate equations and their applications

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Abstract

In this paper, we consider generalized thermoelastic plate equations with Fourier’s law of heat conduction. By introducing a threshold for decay properties of regularity-loss, we investigate decay estimates of solutions with/without regularity-loss in a framework of weighted \(L^1\) spaces without any constraint condition on initial data. Furthermore, asymptotic profiles of solutions are obtained via representations of solutions in the Fourier space, which are performed by employing WKB analysis. Next, we study generalized thermoelastic plate equations with additional structural damping and analyze the influence of structural damping on qualitative properties of solutions. We find that the regularity-loss structure is destroyed by structural damping. Finally, we give some applications of our results on thermoelastic plate equations and Moore–Gibson–Thompson equation with friction.

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Acknowledgements

Yan Liu is supported by the National Natural Science Foundation of China (Grant No. 61907010), Natural Science in Higher Education of Guangdong, China (Grant No. 2018KZDXM048), and the General Project of Science Research of Guangzhou (Grant # 201707010126). The PhD study of Wenhui Chen is supported by Sächsiches Landesgraduiertenstipendium. The authors thank the anonymous referees for carefully reading the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Guangdong University of Finance, 510521, Guangzhou, People’s Republic of China

    Yan Liu

  2. Institute of Applied Analysis, Faculty for Mathematics and Computer Science, Technical University Bergakademie Freiberg, Prüferstraße 9, 09596, Freiberg, Germany

    Wenhui Chen

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  1. Yan Liu
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Correspondence to Wenhui Chen.

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Liu, Y., Chen, W. Asymptotic profiles of solutions for regularity-loss-type generalized thermoelastic plate equations and their applications. Z. Angew. Math. Phys. 71, 55 (2020). https://doi.org/10.1007/s00033-020-1283-z

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  • DOI: https://doi.org/10.1007/s00033-020-1283-z

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