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 Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, Number 3(23), Pages 19–26 (Mi vkam250)

ANALYSIS, DIFFERENTIAL EQUATIONS AND OPTIMUM CONTROL

A boundary value problem with displacement for a model equation of a parabolic-hyperbolic type of the third order

Zh. A. Balkizov

Institute of Applied Mathematics and Automation, 360000, Nalchik, Shortanova st., 89A, Russia

Abstract: In this paper, we study the boundary-value problem with displacement for a model inhomogeneous parabolic-hyperbolic equation of the third order. We prove the uniqueness and existence theorems for a regular solution of the problem under study. In the case when the coefficients of the problem are constant real numbers, the solution of the problem under study is written out in explicit form.

Keywords: mixed type equation, boundary-value problem with displacement, thirdorder equation with multiple characteristics, Tricomi method, method of integral equations.

DOI: https://doi.org/10.18454/2079-6641-2018-23-3-19-26

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UDC: 517.95
MSC: 35M12

Citation: Zh. A. Balkizov, “A boundary value problem with displacement for a model equation of a parabolic-hyperbolic type of the third order”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, no. 3(23), 19–26

Citation in format AMSBIB
\Bibitem{Bal18} \by Zh.~A.~Balkizov \paper A boundary value problem with displacement for a model equation of a parabolic-hyperbolic type of the third order \jour Vestnik KRAUNC. Fiz.-Mat. Nauki \yr 2018 \issue 3(23) \pages 19--26 \mathnet{http://mi.mathnet.ru/vkam250} \crossref{https://doi.org/10.18454/2079-6641-2018-23-3-19-26} \elib{https://elibrary.ru/item.asp?id=35604465} 

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This publication is cited in the following articles:
1. Zh. A. Balkizov, “On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:2 (2020), 211–225
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