graphs, eigenvalues and eigenfunctions, discrete and self-conjugate operators, regularized trace method, Galerkin method
Abstract
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.
Author Biographies
Sergey Ivanovich Kadchenko, Nosov Magnitogorsk State Technical University, Magnitogorsk
Dr. Sc. (Physics and Mathematics), Professor, Applied Mathematics and Informatics Department
Lyubov' Sergeevna Ryazanova, Nosov Magnitogorsk State Technical University, Magnitogorsk
Cand. Sc. (Pedagogical), Associate Professor, Department of Applied Mathematics and Informatics
