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Global Stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers
- Source :
- Kalantarov, VK; & Titi, ES. (2017). Global Stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers. UC Irvine: Retrieved from: http://www.escholarship.org/uc/item/7cx1h4jh
- Publication Year :
- 2017
- Publisher :
- eScholarship, University of California, 2017.
-
Abstract
- In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped nonlinear wave equations and the nonlinear wave equation with nonlinear damping term, the Benjamin-Bona-Mahony-Burgers equation and the KdV-Burgers equation. This algorithm capitalizes on the fact that such infinite-dimensional dissipative dynamical systems posses finite-dimensional long-time behavior which is represented by, for instance, the finitely many determining parameters of their long-time dynamics, such as determining Fourier modes, determining volume elements, determining nodes , etc..The algorithm utilizes these finite parameters in the form of feedback control to stabilize the relevant solutions. For the sake of clarity, and in order to fix ideas, we focus in this work on the case of low Fourier modes feedback controller, however, our results and tools are equally valid for using other feedback controllers employing other spatial coarse mesh interpolants.
- Subjects :
- 0209 industrial biotechnology
Work (thermodynamics)
Mathematics::Analysis of PDEs
02 engineering and technology
01 natural sciences
symbols.namesake
Mathematics - Analysis of PDEs
020901 industrial engineering & automation
Control theory
FOS: Mathematics
Discrete Mathematics and Combinatorics
Applied mathematics
0101 mathematics
Navier–Stokes equations
Finite set
math.AP
Mathematics
Applied Mathematics
010102 general mathematics
Order (ring theory)
Term (time)
Nonlinear system
Fourier transform
symbols
Focus (optics)
Analysis of PDEs (math.AP)
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Kalantarov, VK; & Titi, ES. (2017). Global Stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers. UC Irvine: Retrieved from: http://www.escholarship.org/uc/item/7cx1h4jh
- Accession number :
- edsair.doi.dedup.....83fdda5a28b78b0610365467117b1f9a