We show the existence of insensitizing controls and study null controllability with constraints for the Burgers equation. We solve these problems by first considering the linearized problem, then, by the Kakutani fixed point theorem, we show that the same results hold for the Burgers equation. The main difficulty in this paper is dealing with the nonlinear term in the Burgers equation.
"Some control problems for the Burgers equation." Rocky Mountain J. Math. 50 (2) 559 - 581, April 2020. https://doi.org/10.1216/rmj.2020.50.559