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The Dirichlet problem for telegraph equation in a rectangular domain

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Abstract

We investigate the Dirichlet problem for the telegraph equation in a rectangular domain. We establish a criterion of uniqueness of solution to the problem. The solution is constructed as the sum of an orthogonal series. In substantiation of convergence of the series, the problem of small denominators occurs. In connection with this, we establish estimates ensuring separation from zero of denominators with the corresponding asymptotics which allow us to prove the existence of a regular solution and prove its stability under small perturbations of boundary functions.

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Authors and Affiliations

  1. Sterlitamak Branch of Bashkir State University, pr. Lenina 49, Sterlitamak, 453100, Russia

    Yu. K. Sabitova

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  1. Yu. K. Sabitova
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Correspondence to Yu. K. Sabitova.

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Original Russian Text © Yu.K. Sabitova, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 12, pp. 46–56.

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Sabitova, Y.K. The Dirichlet problem for telegraph equation in a rectangular domain. Russ Math. 61, 39–48 (2017). https://doi.org/10.3103/S1066369X17120052

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