Controllability of nonlinear PDE’s: Agrachev–Sarychev approach
Armen Shirikyan1
1CNRS (UMR 8088), Département de Mathématiques Université de Cergy–Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin 95302 Cergy–Pontoise Cedex, France
Journées équations aux dérivées partielles (2007), article no. 4, 11 p.

This short note is devoted to a discussion of a general approach to controllability of PDE’s introduced by Agrachev and Sarychev in 2005. We use the example of a 1D Burgers equation to illustrate the main ideas. It is proved that the problem in question is controllable in an appropriate sense by a two-dimensional external force. This result is not new and was proved earlier in the papers [AS05, AS07] in a more complicated situation of 2D Navier–Stokes equations.

DOI: 10.5802/jedp.43
Classification: 35Q35, 93B05, 93C20
Keywords: Burgers equation, approximate controllability, exact controllability in projection, Agrachev–Sarychev method

Armen Shirikyan  1

1 CNRS (UMR 8088), Département de Mathématiques Université de Cergy–Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin 95302 Cergy–Pontoise Cedex, France 
Armen Shirikyan. Controllability of nonlinear PDE’s: Agrachev–Sarychev approach. Journées équations aux dérivées partielles (2007), article  no. 4, 11 p.. doi: 10.5802/jedp.43
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