2019
DOI: 10.1137/18m1172405
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Feedback Stabilization of a Two-Dimensional Fluid-Structure Interaction System with Mixed Boundary Conditions

Abstract: We study the stabilization of a fluid-structure interaction system around an unstable stationary solution. The system consists of coupling the incompressible Navier-Stokes equations, in a two dimensional polygonal domain with mixed boundary conditions, and a damped Euler-Bernoulli beam equations located at the boundary of the fluid domain. The control acts only in the beam equations. The feedback is determined by stabilizing the projection of the linearized model onto a finite dimensional invariant subspace. H… Show more

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Cited by 3 publications
(1 citation statement)
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“…In [21], the second author has studied the stabilization of a fluid-structure model in two dimensions, where the structure is a damped beam equation located at the boundary of the fluid domain. These results have been recently extended to more complex systems, see [7]. We also mention [9,10], where the shape of an elastic structure is used to reduce the drag of a fluid flow surrounding this an elastic structure.…”
Section: Setting Of the Problemmentioning
confidence: 91%
“…In [21], the second author has studied the stabilization of a fluid-structure model in two dimensions, where the structure is a damped beam equation located at the boundary of the fluid domain. These results have been recently extended to more complex systems, see [7]. We also mention [9,10], where the shape of an elastic structure is used to reduce the drag of a fluid flow surrounding this an elastic structure.…”
Section: Setting Of the Problemmentioning
confidence: 91%