  We give a survey of recent results on 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 considered. The
focus of the discussion here is on the interesting mathematical aspects of
physical phenomena occurring in aeroelasticity, such as flutter and divergence.
This leads to a partial differential equation (PDE) treatment of issues such as
well-posedness of finite energy solutions, and long-time (asymptotic) behavior.
The latter includes theory of asymptotic stability, convergence to equilibria,
and to global attracting sets. We complete the discussion with several well
known observations and conjectures based on experimental/numerical studies.
