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Nonlinear feedback stabilization of a two-dimensional Burgers equation

This article investigates the important problem of nonlinear feedback synthesis for the stabilization of a two-dimensional Burgers equation. It is relevant in particular because it contains some key ingredients that arise in the control of two-dimensional Navier-Stokes equations

The article is a significant step in the direction of developing control laws for nonlinear partial differential equations that guarantee more than infinitesimally local stability results. The authors achieve stabilization for any stationary profile of the Burgers equation using a nonlinear feedback law. The numerical simulations show that this nonlinear feedback permits to stabilize the system in some situations where a classical linear one does not.

Emmanuel Trélat
Editor

Nonlinear feedback stabilization of a two-dimensional Burgers equation
Laetitia Thevenet, Jean-Marie Buchot and Jean-Pierre Raymond
ESAIM: COCV 16 (2010) 929-955
DOI: http://dx.doi.org/10.1051/cocv/2009028