W. T. and Idalia Reid Prize in Mathematics Lec- ture: Analysis and Control of Coupled PDE Sys- tems Arising in Fluid- Structure and Gas Flow- Structure Interactions

Interactive systems comprising nonlinear dynamics which evolve in two media and are coupled at their interface arise in a variety of applications. These include utter control and suppression in aeroelasticity in both subsonic and super-sonic regimes; noise reduction in an acoustic chamber; con-trol of oscillations in fluid-structure interaction, etc. The benchmark models describing the dynamics of these com-plex systems consist of coupled PDE equations, possibly of different type, say parabolic versus hyperbolic. Coupling takes place at the interface separating the two media. One challenge is then to place a controller localized at such in-terface for the purpose of achieving a desired performance of the overall coupled system. This leads to interesting mathematical questions such as the analysis of short and long time behavior of the underlying PDE’s and their inter-action via interface. This lecture will present several new developments in this area and will also underscore open questions