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The First Boundary Problem with an Integral Condition for a Mixed-Type Equation with a Characteristic Degeneration

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Abstract

In this paper, we study the first boundary problem for a mixed-type elliptic-hyperbolic equation of the second kind in a rectangular domain. We construct the problem solution as the sum of a biorthogonal series and prove the uniqueness criterion for it. When proving the existence of the problem solution, we encounter the problem of small denominators. In this connection, we establish estimates for the separation of denominators from zero with the corresponding asymptotics; this allows us to justify the existence of a solution in the class of regular solutions.

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Funding

This work was supported by the Russian Foundation for Basic Research, nos. 17-41-020-516, 18-31-00111.

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Authors and Affiliations

  1. Sterlitamak Branch of Bashkir State University, 49 Lenin ave., 453100, Sterlitamak, Russia

    Yu. K. Sabitova

  2. Sterlitamak Branch of the Institute for Strategic Studies of the Republic of Bashkortostan, 68 Odesskaya str., 453103, Sterlitamak, 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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Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 11, pp. 46–64.

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Sabitova, Y.K. The First Boundary Problem with an Integral Condition for a Mixed-Type Equation with a Characteristic Degeneration. Russ Math. 64, 39–57 (2020). https://doi.org/10.3103/S1066369X20110043

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  • DOI: https://doi.org/10.3103/S1066369X20110043

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