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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 9, Pages 14–29
DOI: https://doi.org/10.26907/0021-3446-2022-9-14-29 (Mi ivm9808) 		 
This article is cited in 4 scientific papers (total in 4 papers)

A boundary value problem with a conormal derivative for the mixed type equation of second kind with a conjugation condition of the Frankl type

B. I. Islomova, A. A. Abdullayevb

a National University of Uzbekistan named after M.Ulugbek, 4 University str., Tashkent, 700174 Republic of Uzbekistan
b Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 Kari Niyazi str., Tashkent, 100000 Republic of Uzbekistan
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DOI: https://doi.org/10.26907/0021-3446-2022-9-14-29
Abstract: In this paper, using the properties of generalized solutions, both in the hyperbolic part and in the elliptic part of the mixed domain, we study a boundary value problem with a conormal derivative for a mixed type equation of the second kind with Frankl type conditions is investigated. The uniqueness of the solution to the problem under study is proved using the extremum principle, and the existence is proved by the method of integral equations. The theory of singular integral equations, Wiener-Hopf and Fredholm integral equations of the second kind are used to prove the existence of a solution to the problem.
Keywords: equation of the second kind, extremum principle, Wiener-Hopf equation, convolution-type equation, Green's function, uniqueness and existence of a solution.
Received: 14.11.2021
Revised: 10.02.2022
Accepted: 08.04.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 9, Pages 11–25
DOI: https://doi.org/10.3103/S1066369X2209002X
Document Type: Article
UDC: 517.956
Language: Russian
Citation: B. I. Islomov, A. A. Abdullayev, “A boundary value problem with a conormal derivative for the mixed type equation of second kind with a conjugation condition of the Frankl type”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 9, 14–29; Russian Math. (Iz. VUZ), 66:9 (2022), 11–25
Citation in format AMSBIB
\Bibitem{IslAbd22}
\by B.~I.~Islomov, A.~A.~Abdullayev
\paper A boundary value problem with a conormal derivative for the mixed type equation of second kind with a conjugation condition of the Frankl type
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 9
\pages 14--29
\mathnet{http://mi.mathnet.ru/ivm9808}
\crossref{https://doi.org/10.26907/0021-3446-2022-9-14-29}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 9
\pages 11--25
\crossref{https://doi.org/10.3103/S1066369X2209002X}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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