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.
Keywords:eigenvalues and eigenfunctions; discrete and self-conjugate operators; regularized trace method; Galerkin method.
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