2024/11/19 by Laheurte, Vincent
#93C20 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2411.12267
We consider the one-dimensional Burgers' equation linearized at a stationary shock, and investigate its null-controllability cost with a control at the left endpoint. We give an upper and a lower bound on the control time required for this cost to remain bounded in the vanishing viscosity limit, as well as a rough description of an admissible control. The proof relies on complex analysis and adapts methods previously used to tackle the same issue with a constant transport term.