Abstract:
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.
Keywords:wave equation on geometrical graph, transmission condition, propagation of boundary regime, delays differential equations system, existence and uniqueness of solution, solution formula.
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