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 Proceedings of the YSU, Physical and Mathematial Scineces: Year: Volume: Issue: Page: Find

 Proceedings of the YSU, Physical and Mathematial Scineces, 2016, Issue 3, Pages 70–78 (Mi uzeru278)

Mathematics

Nonlocal problem for a mixed type differential equation in rectangular domain

T. K. Yuldashev

Department of Higher Mathematics, Siberian State Aerospace University, Krasnoyarsk, RF

Abstract: In the article the questions of solvability and construction of the solution of nonlocal mixed value problem for a homogeneous mixed type differential equa tion are considered. The spectral method based on the separation of variables is used. A criterion for a single-valued solvability of the considered problem is installed. Under this criterion the single-valued solvability of the problem is proved. The existence of problem solutions in the case of uniqueness failure is studied, also.

Keywords: mixed value problem, mixed type differential equation, integral condition, one valued solvability.

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Document Type: Article
MSC: Primary 35A02; Secondary 35M10, 35S05
Accepted:18.07.2016
Language: English

Citation: T. K. Yuldashev, “Nonlocal problem for a mixed type differential equation in rectangular domain”, Proceedings of the YSU, Physical and Mathematial Scineces, 2016, no. 3, 70–78

Citation in format AMSBIB
\Bibitem{Yul16} \by T.~K.~Yuldashev \paper Nonlocal problem for a mixed type differential equation in rectangular domain \jour Proceedings of the YSU, Physical and Mathematial Scineces \yr 2016 \issue 3 \pages 70--78 \mathnet{http://mi.mathnet.ru/uzeru278} 

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This publication is cited in the following articles:
1. T. K. Yuldashev, “On an integro-differential equation of pseudoparabolic-pseudohyperbolic type with degenerate kernels”, Uch. zapiski EGU, ser. Fizika i Matematika, 52:1 (2018), 19–26
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