SOLVING FORWARD AND CONTROL PROBLEMS FOR TELEGRAPHER'S EQUATIONS ON METRIC GRAPHS.

In this paper, we solve forward and control problems for telegrapher's equation on metric graphs. The forward problem is considered on general graphs, and an effcient algorithm for solving the equations for a constant inductance and capacitance and for a variable resistance and conductance is developed. The control problem is considered on tree graphs, i.e. graphs without cycles, with some restrictions on the coeffcients. In particular, we consider equations with constant coefficients which do not depend on the edge. We obtained the necessary and sufficient conditions of the exact controllability and indicate the minimal control time. [ABSTRACT FROM AUTHOR]