Analysis of transient acoustic scattering by an elastic obstacle
Abstract
Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two- and three-dimensional acoustic-elastic wave propagation problem in the time-domain. A compressed coordinate transformation is proposed to reduce equivalently the scattering problem into an initial-boundary value problem in a bounded domain over a finite time interval. The reduced problem is shown to have a unique weak solution by using the Galerkin method. The stability estimate and an a priori estimate with explicit time dependence are obtained for the weak solution. The reduced model problem is suitable for numerical simulations. The proposed method is applicable to many other time-domain scattering problems imposed in open domains.
Keywords
Cite
@article{arxiv.1811.12480,
title = {Analysis of transient acoustic scattering by an elastic obstacle},
author = {Peijun Li and Lei Zhang},
journal= {arXiv preprint arXiv:1811.12480},
year = {2018}
}