Analysis of transient acoustic scattering by an elastic obstacle

TL;DR

This paper presents a mathematical framework for analyzing transient acoustic scattering by elastic obstacles, introducing a coordinate transformation and proving solution existence, stability, and suitability for numerical simulation.

Contribution

It proposes a novel coordinate transformation to reduce the scattering problem to a bounded domain and establishes the existence, uniqueness, and stability of solutions in the time domain.

Findings

Unique weak solution established for the reduced problem

Stability and a priori estimates with explicit time dependence derived

Method applicable to various time-domain scattering problems in open domains

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.