Cost of Controllability of the Burgers Equation Linearized at a Steady Shock in the Vanishing Viscosity Limit
Abstract
Abstract. 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, and we construct an admissible control with an explicit limit behavior. We also provide an extension of the analysis to the case where the control acts on both endpoints. The proof relies on complex analysis and adapts methods previously used to tackle the same issue with a constant transport term.
Fields of Study & Subjects
Fluid Dynamics and Turbulent Flows
Gas Dynamics and Kinetic Theory
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 3
- Pages
- 2702–2737
- Publication date
- 27 May 2026
- Language
- EN