Analysis, Control and Inverse Theory of Fluids,Waves, Materials Structures, and theirInteractions
Technical Report,01 Jul 2011,30 Jun 2015
University of Virginia Charlottesville United States
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The focus of this research is multi-fold Fluids, waves, structures and their interrelationships. This research made advances on all fronts. Regarding fluid, it solved the problem of feedback stabilization of the Navier-Stokes equations by tangential controls with arbitrarily small support. Moreover, it study fluid-structure interaction models when either the structures moves within the immersed fluid or else is static but has small andrapid oscillations. In addition, this research produced a theoretical solution to the problem of flutter suppression of a flow of gas over a panel, sayan aircraft wing, at the subsonic regime, by means of inserting suitable friction on the structure only. In the supersonic regime, the problem of controlling flutter can be reduced to a finite dimensional problem after a long time. Finally, this research solved the inverse problem of recovering theelectric coefficient of a Schrodinger equation defined on a Riemannian manifold so that also the variable coefficient case in included by meansof just one boundary observationmeasurement acting on a suitable part of the boundary and for an arbitrarily short time interval. here recoverymeans uniqueness of the recovery and stability wekll-posednes of the recovery by using a boundary trace of the solution.
- Fluid Mechanics