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

B. Kanguzhin<sup>ab

a</sup> Institute of Mathematics and Mathematical Modeling, Republic of Kazakhstan
^b Kazakh National University named after Al-Farabi, 71 Al-Farabi Avenue, 050000 Almaty, Republic of Kazakhstan

Abstract: The paper studies the spread of waves along the star graph. The continuation of the initial data from the graph edges for the entire numerical axis allows 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.

Keywords and phrases: star graph, d'Alembert formula, eigenvalues problem, matching conditions.

MSC: 34A55, 34B05, 58C40

Received: 10.09.2024

Language: English

DOI: 10.32523/2077-9879-2025-16-4-45-53