Solution to the Dirichlet Problem of the Wave Equation on a Star Graph
Gaukhar Arepova,
Ludmila Alexeyeva,
Dana Arepova
Abstract:In this paper, the solution to the Dirichlet problem for the wave equation on the star graph is constructed. To begin, we solve the boundary value problem on the interval (on one edge of the graph). We use the generalized functions method to obtain the wave equation with a singular right-hand side. The solution to the Dirichlet problem is determined through the convolution of the fundamental solution with the singular right-hand side of the wave equation. Thus, the solution found on the interval is determined … Show more
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