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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 210, Pages 12–23
DOI: https://doi.org/10.36535/0233-6723-2022-210-12-23 (Mi into1011) 		 
On the solvability of boundary-value problems for third-order equations of parabolic-hyperbolic type with lower terms

O. Kh. Abdullaeva, A. A. Matchanovab

a V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan
b Institute of Ion-Plasma and Laser Technologies, Uzbekistan Academy of Sciences, Tashkent
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DOI: https://doi.org/10.36535/0233-6723-2022-210-12-23
Abstract: In this paper, boundary-value problems for a third-order mixed differential equation of the parabolic-hyperbolic type with a fractional Gerasimov–Caputo operator are examined. Classes of functions that ensure the unique solvability of the boundary-value problem are found. The existence and uniqueness of a solution of the boundary-value problem are proved.
Keywords: parabolic-hyperbolic equation, Gerasimov–Caputo differential operator, integral equation, uniqueness of solution, existence of solution.
Document Type: Article
UDC: 517.967
MSC: 35М10, 34К37, 35R11, 35D30
Language: Russian
Citation: O. Kh. Abdullaev, A. A. Matchanova, “On the solvability of boundary-value problems for third-order equations of parabolic-hyperbolic type with lower terms”, Geometry, Mechanics, and Differential Equations, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 210, VINITI, Moscow, 2022, 12–23
Citation in format AMSBIB
\Bibitem{AbdMat22}
\by O.~Kh.~Abdullaev, A.~A.~Matchanova
\paper On the solvability of boundary-value problems for third-order equations of parabolic-hyperbolic type with lower terms
\inbook Geometry, Mechanics, and Differential Equations
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 210
\pages 12--23
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1011}
\crossref{https://doi.org/10.36535/0233-6723-2022-210-12-23}
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