Flow-plate interactions: Well-posedness and long-time behavior


We consider ow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic ow velocities are treated with Neumann type ow conditions, and a novel treatment of the so called Kutta-Joukowsky ow 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 ofinite 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 ow-structure system to a PDE system with delay.

Publication Title

Discrete and Continuous Dynamical Systems - Series S