Boundary Controllability of a Dynamical System Governed by the Wave Equation on a Class of Graphs (Trees)

The boundary control problem for the wave equation on a planar graph consisting of strings of variable densities with Dirichlet control at boundary vertices is considered. The exact controllability in L₂-classes of controls and states is established in the case where the graph is a tree; a sharp estimate of the time of controllability is given. Bibliography: 7 titles. Dedicated to J. E. Lagnese on the occasion of his 65th birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 23–47.