Abstract:
This paper investigates the unique solvability of the boundary control problem for a one-dimensional wave
equation loaded along one of its characteristic curves in terms of a regular solution. The solution method
is based on an analogue of the d’Alembert formula constructed for this equation. We point out that the
domain of definition for the solution of DE, when the initial and final Cauchy data given on intervals of
the same length is a square. The side of the squire is equal to the interval length. The boundary controls
are established by the components of an analogue of the d’Alembert formula, which, in turn, are uniquely
established by the initial and final Cauchy data. It should be noted that the normalized distribution and
centering are employed in the final formulas of sought boundary controls, which is not typical for initial
and boundary value problems initiated by equations of hyperbolic type.
