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Interface Feedback Control Stabilization of a Nonlinear Fluid–Structure Interaction

Hassanzadeh Kelishomi, Mojtaba | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43692 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Hesaraki, Mahmud
  7. Abstract:
  8. In this thesis, We consider a model of a fluid–structure interaction defined on a bounded domain Ω ⊆ R2, that describes a body of elasticity interacting with a fluid. Ω is a bounded simply connected domain, consisting of two open sub-domains Ωs and Ωf .Ωf is the exterior domain with non-overlapping boundaries Γf and Γs, so that ∂Ωs = Γs. Ωs is an interior domain with boundary Γs.Ωs is occupied by an elastic body while Ωf is filled with a fluid.The interaction between the elastic body and the fluid takes place at the interface Γs.The dynamics of the fluid is described by the Navier–Stokes equation and the dynamics of the elastic body is described by an elasto-dynamic system of wave equations. u(t, x) ∈ Rn is a vector-valued function representing the velocity of the fluid and p(t, x) is a scalar-valued function representing the pressure.w(t, x),wt(t, x) ∈ Rn denotes the displacement and the velocity functions of the elastic solid Ωs.ν denotes the unit outward normal vector on Γs with respect to the region Ωs. The model considered accounts for rapid but small oscillations of the elastic displacements. [17]This leads to thefollowing interactive PDEs defined for the state variables (u,w,wt, p) and the associated tensors in (2.1).Our main goal is to determine how fast the energy decays. We are able to show that with the presence of the boundary damping (β > 0), the energy associated with weak solutions to system with initial data in the natural energy space H, goes to zero uniformly at the exponential rate.And when α > 0, the full H norm of the solution decays to zero
  9. Keywords:
  10. Navier-Stokes Equation ; Fluid-Structure Interaction ; Elasticity Systems ; Feedback Boundary Control ; Uniform Stability

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