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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/vsgtu1822
https://www.mathnet.ru/eng/vsgtu/v225/i3/p407
This publication is cited in the following 1 articles:
B. I. Islomov, T. K. Yuldashev, O. M. Yunusov, “Nonlocal Boundary Problem for a Loaded Equation of Mixed Type in a Special Domain”, Lobachevskii J Math, 45:7 (2024), 3304
Citation in format AMSBIB
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