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Analysis of a time-dependent fluid-solid interaction problem above a local rough surface

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Abstract

This paper is concerned with the mathematical analysis of a time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded scattering problem into an equivalent initial-boundary value problem defined in a bounded domain by proposing a transparent boundary condition (TBC) on a hemisphere. Analyzing the reduced problem with the Lax-Milgram lemma and the abstract inversion theorem of the Laplace transform, we prove the well-posedness and stability for the reduced problem. Moreover, an a priori estimate is established directly in the time domain for the acoustic wave and elastic displacement by using the energy method.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11771349), the Fundamental Research Funds for the Central Universities (Grant No. 1191329813), the China Postdoctoral Science Foundation (Grant Nos. 2015M580827 and 2016T90900) and Postdoctoral Research Project of Shaanxi Province of China (Grant No. 2016BSHYDZZ52).

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Changkun Wei

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Changkun Wei

  3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Jiaqing Yang

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  1. Changkun Wei
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  2. Jiaqing Yang
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Correspondence to Jiaqing Yang.

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Wei, C., Yang, J. Analysis of a time-dependent fluid-solid interaction problem above a local rough surface. Sci. China Math. 63, 887–906 (2020). https://doi.org/10.1007/s11425-017-9364-3

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  • DOI: https://doi.org/10.1007/s11425-017-9364-3

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