Expansion in eigenfunctions of the Sturm-Liouville problem on a bundle graph |
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Authors: | V. V. Provotorov |
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Affiliation: | (1) Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia |
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Abstract: | In this paper we consider the applicability of the Fourier method for partial differential equations on spatial grids (we choose a bundle graph as a model). This leads to an important problem, namely, to the expansion of a given function in eigenfunctions of the corresponding Sturm-Liouville problem on a grid. We study a model problem which describes a symmetric case, when one considers physically identical one-dimensional continuums on the bundle graph. Such problems arise, for example, in the modeling of oscillating processes of an elastic mast with supporting elastic ties. |
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Keywords: | boundary-value problem on a graph eigenfunctions the Green function completeness of system of eigenfunctions expansion in eigenfunctions |
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