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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（5）
• 页码范围: 887-906
• 页数: 20页
• 语种: 英文

摘要

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.