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- W2334358552 startingPage "1169" @default.
- W2334358552 abstract "Let $-A: mathcal{D}(A)to H$ be the generator of an analytic semigroup and $B : U to [mathcal{D}(A^*)]'$ a relatively bounded control operator such that $(A-sigma,B)$ is stabilizable for some $sigma>0$. In this paper, we consider the stabilization of the nonlinear system $y'+Ay+G(y,u)=Bu$ by means of a feedback or a dynamical control $u$. The control is obtained from the solution to a Riccati equation which is related to a low-gain optimal quadratic minimization problem. We provide a general abstract framework to define exponentially stable solutions which is based on the contruction of Lyapunov functions. We apply such a theory to stabilize, around an unstable stationary solution, the 2D or 3D Navier-Stokes equations with a Neumann control and the 2D or 3D Boussinesq equations with a Dirichlet control." @default.
- W2334358552 created "2016-06-24" @default.
- W2334358552 creator A5081799880 @default.
- W2334358552 date "2012-01-01" @default.
- W2334358552 modified "2023-10-09" @default.
- W2334358552 title "Abstract settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichlet control" @default.
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- W2334358552 doi "https://doi.org/10.3934/dcds.2012.32.1169" @default.
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