Title :
Boundary asymptotic stabilizability of a nonlinear fluid structure interaction
Author :
Lasiecka, Irena ; Lu, Yongjin
Author_Institution :
Dept. of Math., Univ. of Virginia, Charlottesville, VA, USA
Abstract :
We consider a model of fluid-structure interaction in a bounded domain Ω ∈ ℝ2 where Ω is comprised of two open adjacent domains occupied, respectively, by the solid and the fluid. This leads to a study of Navier Stokes equation coupled on the boundary to the dynamic system of elasticity. We shall consider models when the elastic body exhibits small but rapid oscillations. These are established models arising in engineering applications when the structure is immersed in a viscous flow of liquid. The goal of the work is to present recent results on asymptotic stabilizability of the interactive structure. It will be shown that under suitable geometric conditions imposed on the domain the model is asymptotically stabilizable with a boundary feedback acting as a force on the interface. The required geometric conditions result from the presence of the pressure acting upon the solid.
Keywords :
Navier-Stokes equations; asymptotic stability; boundary layers; elasticity; elastodynamics; fluid oscillations; mechanical variables control; Navier Stokes equation; boundary asymptotic stabilizability; boundary feedback; boundary system; bounded domain; dynamic system; elastic body; elasticity; engineering applications; fluid-structure interaction model; geometric conditions; interactive structure; nonlinear fluid structure interaction; open adjacent domains; rapid oscillations; viscous flow; Asymptotic stability; Convergence; Equations; Mathematical model; Propagation; Solids; Stability analysis;
Conference_Titel :
Decision and Control (CDC), 2010 49th IEEE Conference on
Conference_Location :
Atlanta, GA
Print_ISBN :
978-1-4244-7745-6
DOI :
10.1109/CDC.2010.5717717