| Issue |
ESAIM: COCV
Volume 16, Number 4, October-December 2010
|
|
|---|---|---|
| Page(s) | 929 - 955 | |
| DOI | https://doi.org/10.1051/cocv/2009028 | |
| Published online | 31 July 2009 | |
Nonlinear feedback stabilization of a two-dimensional Burgers equation
Université de Toulouse, UPS, Institut de Mathématiques, UMR CNRS 5219, 31062 Toulouse Cedex 9, France. Laetitia.Thevenet@math.univ-toulouse.fr; jean-marie.buchot@math.univ-toulouse.fr; raymond@math.univ-toulouse.fr
Received:
2
December
2008
Revised:
5
May
2009
In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of the two-dimensional Burgers equation. We end this paper with a few numerical simulations, comparing the performance of the nonlinear law with the linear one.
Mathematics Subject Classification: 93B52 / 93C20 / 93D15
Key words: Dirichlet control / Neumann control / feedback control / stabilization / Burgers equation / Algebraic Riccati equation
© EDP Sciences, SMAI, 2009
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