  We consider flow-structure interactions modeled by a modified wave equation
coupled at an interface with equations of nonlinear elasticity. Both subsonic
and supersonic flow velocities are treated with Neumann type flow conditions,
and a novel treatment of the so called Kutta-Joukowsky flow conditions are
given in the subsonic case. The goal of the paper is threefold: (i) to provide
an accurate review of recent results on existence, uniqueness, and stability of
weak solutions, (ii) to present a construction of finite dimensional,
attracting sets corresponding to the structural dynamics and discuss
convergence of trajectories, and (iii) to state several open questions
associated with the topic. This second task is based on a decoupling technique
which reduces the analysis of the full flow-structure system to a PDE system
with delay.
