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We give a survey of recent results on flow-structure interactions modeled bya modified wave equation coupled at an interface with equations of nonlinearelasticity. Both subsonic and supersonic flow velocities are considered. Thefocus of the discussion here is on the interesting mathematical aspects ofphysical phenomena occurring in aeroelasticity, such as flutter and divergence.This leads to a partial differential equation (PDE) treatment of issues such aswell-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 wellknown observations and conjectures based on experimental/numerical studies.

Von Karman plate in a gas flow: recent results and conjectures