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 Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 8, Pages 43–52 (Mi ivm8730)

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

M. Kh. Ruziev

Department of Differential Equations, Institute of Mathematics and Information Technologies, National Academy of Sciences of Republic of Uzbekistan, Tashkent, Republic of Uzbekistan

Abstract: In this paper we study a 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.

Keywords: extremum principle, unique solvability, existence of solution, integral equations.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:8, 35–43

Bibliographic databases:

UDC: 517.956

Citation: M. Kh. Ruziev, “A problem with the Frankl and Bitsadze–Samarskii condition on the line of degeneracy and on parallel characteristics for a mixed-type equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 8, 43–52; Russian Math. (Iz. VUZ), 56:8 (2012), 35–43

Citation in format AMSBIB
\Bibitem{Ruz12} \by M.~Kh.~Ruziev \paper A problem with the Frankl and Bitsadze--Samarskii condition on the line of degeneracy and on parallel characteristics for a~mixed-type equation \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2012 \issue 8 \pages 43--52 \mathnet{http://mi.mathnet.ru/ivm8730} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3077486} \transl \jour Russian Math. (Iz. VUZ) \yr 2012 \vol 56 \issue 8 \pages 35--43 \crossref{https://doi.org/10.3103/S1066369X12080051} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866244927}