Communications in Mathematical Sciences

Volume 17 (2019)

Number 6

Analysis of transient acoustic scattering by an elastic obstacle

Pages: 1671 – 1698



Peijun Li (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)

Lei Zhang (Department of Mathematics, Heilongjiang University, Harbin, China; and Heilongjiang Provincial Key Laboratory of Complex Systems Theory and Computation, Harbin, China)


Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous medium. This paper concerns the transient analysis of such a coupled acoustic-elastic wave propagation problem. 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 a priori estimates with explicit time dependence are obtained for the weak solution. The proposed method and the reduced model problem are useful for numerical simulations.


time domain, acoustic wave equation, elastic wave equation, well-posedness and stability, a priori estimate

2010 Mathematics Subject Classification

35A15, 78A45

Received 9 November 2018

Accepted 30 June 2019

Published 26 December 2019