Null Controllability and Stabilizability of Compressible Navier-stokes System in One Dimension

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Hosseini Khajouei, Narges Sadat | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50136 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaraki, Mahmoud
Abstract:
In this thesis we study the exponential stabilization of the one dimensional compressible Navier-Stokes system, in a bounded interval locally around a constant steady state by a localized distributed control acting only in the velocity equation. In fact this is an analysis of a paper that published by Shirshendu Chowdhury, Debayan Maity, Mithily Ramaswamy and Jean-Pierre Raymond in Journal of Differential Equations. We determine a linear feedback law able to stabilize a nonlinear transformed system. Coming back to the original nonlinear system, we obtain a nonlinear feedback law able to stabilize locally this nonlinear system. The result is providing feedback control laws stabilizing compressible fluid flows
Keywords:
Distributed Control ; Feedback Control ; Local Stability ; Stabilizable ; Compressible Navier Stokes Equations

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