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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, Issue 3-4, Pages 24–31 (Mi vsgu508)

Mathematics

Dezin nonlocal problem for a mixed-type equation with power degeneration

V. A. Gushchina

Volga region socially-humanitarian academy, 55/57 Maxim Gorky str., Samara, 443090, Russian Federation

Abstract: In this article, for the equation of mixed elliptic-hyperbolic type with a power degeneracy on the transition line in a rectangular area are studied the problem Dezin with periodicity conditions and non-local condition, binding values of the normal derivative on the lower base of the rectangle with the value of the target solution on the line type of study. Necessary and sufficient conditions for the uniqueness of the solution were settled, and the uniqueness of the solution was proved problem on the based on completeness of the system of peculiar functions of one-problem or the peculiar.

Keywords: the degree of degeneracy, the transition line, nonlocal condition, rectangular area, the uniqueness of solution, one-dimensional problem, the uniqueness.

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UDC: 517.95

Citation: V. A. Gushchina, “Dezin nonlocal problem for a mixed-type equation with power degeneration”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, no. 3-4, 24–31

Citation in format AMSBIB
\Bibitem{Gus16} \by V.~A.~Gushchina \paper Dezin nonlocal problem for a mixed-type equation with power degeneration \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2016 \issue 3-4 \pages 24--31 \mathnet{http://mi.mathnet.ru/vsgu508} \elib{https://elibrary.ru/item.asp?id=29389323}