2018/07/24 by Changkun Wei, Jiaqing Yang, Wei, Changkun +1
Engineering · Mathematics · #65C30 #78A46 #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical methods in engineering #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1807.08868
openalex publication_date 2018/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the mathematical analysis of 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 Lax-Milgram lemma and abstract inversion theorem of 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 with using the energy method.