| Abstract: |
| In this paper we study exact controllability for telegrapher`s equations on metric graphs. First we consider trees, i.e. graphs without cycles. For such graphs, Serge Nicaise derived exact controllability from stabilizability without an estimate of the controllability time (``Stabilization and asymptotic behavior of a generalized telegraph equation``, Z. Angew. Math. Phys. 66 (2015), no. 6, 3221--3247). We give a direct proof of controllability and provide a sharp time estimate in the cases when control is supported at all or all but one of the boundary vertices. If control is supported on a smaller number of the boundary vertices, we prove that the system is not exactly controllable in any finite time interval. Then we consider telegrapher`s equations on general compact graphs with control supported at some boundary and internal vertices. We prove the exact controllability of the system with the optimal number of actuators and estimate the sharp controllability time interval. |
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