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Dirichlet Problem for Lavrent’ev–Bitsadze Equation With Loaded Summands

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Abstract

We study the first boundary-value problem for loaded equation of elliptic-hyperbolic type in rectangular domain. We establish a criterion of uniqueness. A solution to the problem is constructed in the formof the sum of a series. In substantiation of existence of a solution to a problem small denominators appear. We obtain the estimates about a separation from zero of denominators with the corresponding asymptotics. They allow to prove existence of a solution in a class of regular solutions.

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Authors and Affiliations

  1. Sterlitamak Branch of Bashkir State University; Sterlitamak Branch of Institute for Strategic Research of Bashkortostan Republic, 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, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 9, pp. 42–58.

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Sabitova, Y.K. Dirichlet Problem for Lavrent’ev–Bitsadze Equation With Loaded Summands. Russ Math. 62, 35–51 (2018). https://doi.org/10.3103/S1066369X18090050

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  • DOI: https://doi.org/10.3103/S1066369X18090050

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