Propagation of nonsmooth waves along a star graph with fixed boundary vertices

Abstract

The paper studies the spread of waves along a star graph. The continuation of the initial data from the graph edges for the entire numerical axis allows one to represent an analogue of the d’Alembert formula for waves on the star graph. At the same time, the continuation of the initial data is closely related to the continuation of the system of its eigenfunctions of the Sturm–Liouville problem originally defined on the star graph. The continuation of the eigenfunctions defined on the star graph is based on the continuation of the initial data of the mixed problem for the wave equation. The indicated continuation of the initial data of the mixed problem was proposed by B. M. Levitan.