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@unpublished{faucris.319275701,
abstract = {We study the controllability properties of the transport equation and of parabolic equations
posed on a tree. Using a control localized on the exterior nodes, we prove that the hyperbolic and the
parabolic systems are null-controllable. The hyperbolic proof relies on the method of characteristics, the
parabolic one on duality arguments and Carleman inequalities. We also show that the parabolic system may
not be controllable if we do not act on all exterior vertices because of symmetries. Moreover, we estimate the
cost of the null-controllability of transport-diffusion equations with diffusivity ε > 0 and study its asymptotic
behavior when ε → 0
+. We prove that the cost of the controllability decays for a time sufficiently large and
explodes for short times. This is done by duality arguments allowing to reduce the problem to obtain
observability estimates which depend on the viscosity parameter. These are derived by using Agmon and
Carleman inequalities.