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A problem with the Frankl and Bitsadze-Samarskii condition on the line of degeneracy and on parallel characteristics for a mixed-type equation

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Abstract

In this paper we study the boundary-value problem with the Frankl and Bitsadze-Samarskii condition on the line of degeneracy and on parallel characteristics for a mixed-type equation with a singular coefficient. We prove the existence of a solution by the method of integral equations, and we do its uniqueness with the help of the extremum principle.

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Authors and Affiliations

  1. Institute of Mathematics and Information Technologies, National Academy of Sciences of Republic of Uzbekistan, ul. Durman yuli 29, Tashkent, 100125, Republic of Uzbekistan

    M. Kh. Ruziev

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  1. M. Kh. Ruziev
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Correspondence to M. Kh. Ruziev.

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Original Russian Text © M.Kh. Ruziev, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 8, pp. 43–52.

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Ruziev, M.K. A problem with the Frankl and Bitsadze-Samarskii condition on the line of degeneracy and on parallel characteristics for a mixed-type equation. Russ Math. 56, 35–43 (2012). https://doi.org/10.3103/S1066369X12080051

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  • DOI: https://doi.org/10.3103/S1066369X12080051

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