Control Theory for the 1D Burgers Equations on a Linear Planar Network
The paper is devoted to studying the controllability for 1D Burgers equations on a linear planar network with transmission conditions at the interior nodes and with homogeneous Dirichlet on the boundary. More precisely, we show that the Burgers system is approximately controllable and exactly controllable in projections by a finite-dimensional external force. The proof of these results are based on an adaptation of the Agrachev-Sarychev approach to the case of a linear planar network. We would like emphasize that some of the results in this paper are inspired by  in the case of one interval, and by [1, 2] in the case of 2D Navier-Stokes equations.