Controllability of nonlinear PDE’s: Agrachev–Sarychev approach
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.

Classification:  35Q35,  93B05,  93C20
Keywords: Burgers equation, approximate controllability, exact controllability in projection, Agrachev–Sarychev method
     author = {Shirikyan, Armen},
     title = {Controllability of nonlinear PDE's: Agrachev--Sarychev approach},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2007},
     doi = {10.5802/jedp.43},
     language = {en},
     url = {}
Shirikyan, Armen. 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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