PROPAGATION OF NONSMOOTH WAVES ALONG A STAR GRAPH WITH FIXED BOUNDARY VERTICES
Kanguzhin B.
January 2025L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2025#16Issue 445 - 53 pp.
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.
d’Alembert formula , eigenvalues problem , matching conditions , star graph
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