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.
@article{JEDP_2007____A4_0,
author = {Shirikyan, Armen},
title = {Controllability of nonlinear PDE's: Agrachev--Sarychev approach},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
year = {2007},
pages = {1-11},
doi = {10.5802/jedp.43},
language = {en},
url = {http://dml.mathdoc.fr/item/JEDP_2007____A4_0}
}
Shirikyan, Armen. Controllability of nonlinear PDE’s: Agrachev–Sarychev approach. Journées équations aux dérivées partielles, (2007), pp. 1-11. doi : 10.5802/jedp.43. http://gdmltest.u-ga.fr/item/JEDP_2007____A4_0/
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