On the global polynomial stabilization and observation with optimal decay rate

2021 ◽  
Vol 153 ◽  
pp. 111447
Author(s):  
Chaker Jammazi ◽  
Mohamed Boutayeb ◽  
Ghada Bouamaied
Keyword(s):  
Decay Rate ◽  
Optimal Decay ◽  
Optimal Decay Rate ◽  
Polynomial Stabilization

Porous elastic system with Kelvin–Voigt: analyticity and optimal decay rate

2020 ◽  
pp. 1-18
Author(s):  
M. L. S. Oliveira ◽  
E. S. Maciel ◽  
M. J. Dos Santos
Keyword(s):  
Decay Rate ◽  
Elastic System ◽  
Optimal Decay ◽  
Optimal Decay Rate

scholarly journals The optimal decay rate for a weak dissipative Bresse system

2012 ◽  
Vol 25 (3) ◽  
pp. 600-604 ◽  
Author(s):  
Luci Harue Fatori ◽  
Rodrigo Nunes Monteiro
Keyword(s):  
Decay Rate ◽  
Bresse System ◽  
Optimal Decay ◽  
Optimal Decay Rate

scholarly journals Metastability and rapid convergence to quasi-stationary bar states for the two-dimensional Navier–Stokes equations

2013 ◽  
Vol 143 (5) ◽  
pp. 905-927 ◽  
Author(s):  
Margaret Beck ◽  
C. Eugene Wayne
Keyword(s):  
Decay Rate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Optimal Decay ◽  
Optimal Decay Rate ◽  
Long Time ◽  
High Reynolds

Quasi-stationary, or metastable, states play an important role in two-dimensional turbulent fluid flows, where they often emerge on timescales much shorter than the viscous timescale, and then dominate the dynamics for very long time intervals. In this paper we propose a dynamical systems explanation of the metastability of an explicit family of solutions, referred to as bar states, of the two-dimensional incompressible Navier–Stokes equation on the torus. These states are physically relevant because they are associated with certain maximum entropy solutions of the Euler equations, and they have been observed as one type of metastable state in numerical studies of two-dimensional turbulence. For small viscosity (high Reynolds number), these states are quasi-stationary in the sense that they decay on the slow, viscous timescale. Linearization about these states leads to a time-dependent operator. We show that if we approximate this operator by dropping a higher-order, non-local term, it produces a decay rate much faster than the viscous decay rate. We also provide numerical evidence that the same result holds for the full linear operator, and that our theoretical results give the optimal decay rate in this setting.

Stabilisation of stochastic systems with optimal decay rate

2008 ◽  
Vol 2 (1) ◽  
pp. 1-6 ◽  
Author(s):  
J. Feng ◽  
S. Xu ◽  
J. Lam ◽  
Z. Shu
Keyword(s):  
Decay Rate ◽  
Stochastic Systems ◽  
Optimal Decay ◽  
Optimal Decay Rate
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