Steklov Institute of Mathematics at St.Petersburg

PREPRINT 15/2003

ON BOUNDARY CONTROLLABILITY OF DYNAMICAL SYSTEM GOUVERNED BY THE WAVE EQUATION ON A CLASS OF GRAPHS (TREES)

This preprint was accepted October 26, 2003

ABSTRACT:
The boundary control problem for the wave equation on a
planar graph consisting of strings of variable densities
with Dirichlet control at the boundary vertices
is considered. The exact controllability in
$L_2$-classes of controls and states is established in
the case that the grapf is a tree; a sharp estimate of
the time of controllability is given.