De Nitti, NicolaZuazua, Enrique2025-07-112025-07-112023-01-04De Nitti, N., & Zuazua, E. (2023). On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods. Vietnam Journal of Mathematics, 51(1), 71-88. https://doi.org/10.1007/S10013-022-00598-92305-221X10.1007/S10013-022-00598-9https://hdl.handle.net/20.500.14454/3199In this note, we prove a controllability result for entropy solutions of scalar conservation laws on a star-shaped graph. Using a Lyapunov-type approach, we show that, under a monotonicity assumption on the flux, if u and v are two entropy solutions corresponding to different initial data and same in-flux boundary data (at the exterior nodes of the star-shaped graph), then u ≡ v for a sufficiently large time. In order words, we can drive u to the target profile v in a sufficiently large control time by inputting the trace of v at the exterior nodes as in-flux boundary data for u. This result can also be shown to hold on tree-shaped networks by an inductive argument. We illustrate the result with some numerical simulations.eng© The Author(s) 2023ControllabilityEntropy solutionsLyapunovNetworksScalar conservation lawsStar-shaped graphsTree-shaped graphsjournal article2025-07-112305-2228