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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2021, Volume 25, Number 3, Pages 407–422
DOI: https://doi.org/10.14498/vsgtu1822 (Mi vsgtu1822) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differential Equations and Mathematical Physics

On a nonlocal boundary-value problem for a loaded parabolic-hyperbolic equation with three lines of degeneracy

B. I. Islomova, J. A. Xolbekovb

a National University of Uzbekistan named after M. Ulugbek, Tashkent, 100174, Uzbekistan
b Tashkent State Technical University named after I. Karimov, Tashkent, 100174, Uzbekistan
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DOI: https://doi.org/10.14498/vsgtu1822
Abstract: The work is devoted to the proof of the uniqueness and existence of a solution of a nonlocal problem for a loaded parabolic-hyperbolic equation with three lines of change of type. Using the representation of the general solution, the uniqueness of the solution is proved, and the existence of the solution is proved by the method of integral equations. Necessary conditions for the parameters and specified functions are established for the unique solvability of Volterra integral equations of the second kind with a shift equivalent to the problem under study.
Keywords: loaded equation, nonlocal problem, Volterra integral equation with a shift, Green's function, uniqueness and existence of a solution.
Received: August 22, 2020
Revised: May 15, 2021
Accepted: June 28, 2021
First online: September 20, 2021
Bibliographic databases:
Document Type: Article
UDC: 517.956.6
MSC: 35M10
Language: Russian
Citation: B. I. Islomov, J. A. Xolbekov, “On a nonlocal boundary-value problem for a loaded parabolic-hyperbolic equation with three lines of degeneracy”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 25:3 (2021), 407–422
Citation in format AMSBIB
\Bibitem{IslXol21}
\by B.~I.~Islomov, J.~A.~Xolbekov
\paper On a nonlocal boundary-value problem for a loaded parabolic-hyperbolic equation with three lines of degeneracy
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2021
\vol 25
\issue 3
\pages 407--422
\mathnet{http://mi.mathnet.ru/vsgtu1822}
\crossref{https://doi.org/10.14498/vsgtu1822}
\zmath{https://zbmath.org/?q=an:7499951}
\elib{https://elibrary.ru/item.asp?id=46801513}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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