The problem of determining the manner in which an incoming acoustic wave is
scattered by an elastic body immersed in a fluid is one of central importance
in detecting and identifying submerged objects. The problem is generally
referred to as a fluid-structure interaction and is mathematically formulated
as a time-dependent transmission problem. In this paper, we consider a typical
fluid-structure interaction problem by using a coupling procedure which reduces
the problem to a nonlocal initial-boundary problem in the elastic body with a
system of integral equations on the interface between the domains occupied by
the elastic body and the fluid. We analyze this nonlocal problem by the Lubich
approach via the Laplace transform, an essential feature of which is that it
works directly on data in the time domain rather than in the transformed
domain. Our results may serve as a mathematical foundation for treating
time-dependent fluid-structure interaction problems by convolution quadrature
coupling of FEM and BEM