The boundary regimes method in solving of the initial-boundary value problem for the wave equation on a geometrical graph

An approach to describing the solution of the initial-boundary value problem for the wave equation on a finite and bounded geometrical graph \(\Gamma\) is implemented. The linear transmission conditions have a more general form than that considered in previous works. The approach is based on interpreting the behavior of the solution at the vertices of \(\Gamma\) as boundary regimes with respect to adjacent edges. The set of these boundary regimes turns out to be a solution to the initial value problem for a system of delays differential equations on \([0;+\infty)\) with the number of delaying arguments infinitely increasing with infinitely increasing of the argument.