Abstract
In this paper, we consider coupled plate equations with indirect damping including friction and structural damping. By using suitable diagonalization procedure associated with WKB analysis, we derive asymptotic behavior of solutions in the Fourier space. Then, smoothing effect and decay properties in the \(L^p-L^q\) framework of solutions are derived by employing Fourier analysis and representation of solution. We investigate several thresholds to describe smoothing effect and different types of decay properties, for example, Gevrey smoothing and regularity-loss. Finally, we derive approximation of solutions by finding the gained decay rate.
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Acknowledgements
The authors thank Wenhui Chen (Shanghai Jiao Tong University) for the communications and suggestions in the preparation of the paper. The work is supported by the Foundation of Guangdong Education Department, China (Grant No. 2020TSZK005), and the General Project of Science Research of Guangzhou (Grant # 201707010126).
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Liu, Y., Shi, J. Coupled plate equations with indirect damping: smoothing effect, decay properties and approximation. Z. Angew. Math. Phys. 73, 11 (2022). https://doi.org/10.1007/s00033-021-01640-5
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DOI: https://doi.org/10.1007/s00033-021-01640-5