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@article{faucris.287354212,
abstract = {In 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.