Analysis of a time-dependent fluid-solid interaction problem above a local rough surface |
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Authors: | Wei Changkun Yang Jiaqing |
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Institution: | 1.Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China ;2.School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China ;3.School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China ; |
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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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