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.
Keywords: Burgers equation, approximate controllability, exact controllability in projection, Agrachev–Sarychev method
@article{JEDP_2007____A4_0,
author = {Shirikyan, Armen},
title = {Controllability of nonlinear {PDE{\textquoteright}s:} {Agrachev{\textendash}Sarychev} approach},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {4},
pages = {1--11},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2007},
doi = {10.5802/jedp.43},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.43/}
}
TY - JOUR AU - Shirikyan, Armen TI - Controllability of nonlinear PDE’s: Agrachev–Sarychev approach JO - Journées équations aux dérivées partielles PY - 2007 SP - 1 EP - 11 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.43/ DO - 10.5802/jedp.43 LA - en ID - JEDP_2007____A4_0 ER -
%0 Journal Article %A Shirikyan, Armen %T Controllability of nonlinear PDE’s: Agrachev–Sarychev approach %J Journées équations aux dérivées partielles %D 2007 %P 1-11 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.43/ %R 10.5802/jedp.43 %G en %F JEDP_2007____A4_0
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. http://www.numdam.org/articles/10.5802/jedp.43/
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