Algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a graph with varying edges
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 29-34
Voir la notice de l'article provenant de la source Math-Net.Ru
The paper develops algorithms for calculating the eigenvalues of initial-boundary value
problems for a wave differential equation set in a star graph with time-varying edge lengths. The change
of variables helped to reduce the considered spectral problems to initial-boundary value problems with
fixed edges. The obtained formulas were used to find eigenvalues for a wave differential equation set in
a star graph with time-varying edges with any ordinal numbers. The formulas for calculating the eigenvalues will allow developing algorithms for solving inverse spectral problems set in quantum graphs
with varying edges.
Keywords:
eigenvalues and eigenfunctions; discrete and self-conjugate operators; regularized trace method; Galerkin method.
@article{VYURM_2024_16_4_a3,
author = {S. I. Kadchenko and L. S. Ryazanova},
title = {Algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a graph with varying edges},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
pages = {29--34},
publisher = {mathdoc},
volume = {16},
number = {4},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VYURM_2024_16_4_a3/}
}
TY - JOUR AU - S. I. Kadchenko AU - L. S. Ryazanova TI - Algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a graph with varying edges JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika PY - 2024 SP - 29 EP - 34 VL - 16 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VYURM_2024_16_4_a3/ LA - ru ID - VYURM_2024_16_4_a3 ER -
%0 Journal Article %A S. I. Kadchenko %A L. S. Ryazanova %T Algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a graph with varying edges %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika %D 2024 %P 29-34 %V 16 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURM_2024_16_4_a3/ %G ru %F VYURM_2024_16_4_a3
S. I. Kadchenko; L. S. Ryazanova. Algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a graph with varying edges. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 29-34. http://geodesic.mathdoc.fr/item/VYURM_2024_16_4_a3/