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Fourier method in a mixed problem for the wave equation on a graph

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Abstract

A mixed problem for the wave equation on the simplest geometric graph consisting of two ring edges that touch at a point is considered. The approach used is based on the contour integration of the operator’s resolvent. With the help of a special transformation of a formal series, a classical solution of the problem is obtained under minimum conditions imposed on the initial data. This approach makes it possible to do without an expensive analysis of improved asymptotics for the eigenvalues and eigenfunctions of the operator and to avoid the difficulties associated with the possible multiplicity of the operator’s spectrum.

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Authors and Affiliations

  1. Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia

    M. Sh. Burlutskaya

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  1. M. Sh. Burlutskaya
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Correspondence to M. Sh. Burlutskaya.

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Original Russian Text © M.Sh. Burlutskaya, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 5, pp. 519–522.

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Burlutskaya, M.S. Fourier method in a mixed problem for the wave equation on a graph. Dokl. Math. 92, 735–738 (2015). https://doi.org/10.1134/S1064562415060277

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  • DOI: https://doi.org/10.1134/S1064562415060277

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