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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2016, Volume 20, Number 1, Pages 22–32 (Mi vsgtu1470)  

This article is cited in 1 scientific paper (total in 1 paper)

Differential Equations and Mathematical Physics

The nonlocal A. A. Desin's problem for an equation of mixed elliptic-hyperbolic type

V. A. Gushchina

Samara State University of Social Sciences and Humanities, Samara, 443099, Russian Federation

Abstract: In this paper for the equation of mixed elliptic-hyperbolic type in rectangular area the task with the conditions of periodicity and the nonlocal problem of A. A. Desin was studied, the uniqueness criterion was set. The solution of the problem was constructed as a sum of orthogonal series in eigenfunctions of the corresponding one-dimensional spectral problem. The problem of small denominators arises in justifying the convergence of the series. Therefore the evaluation on the separation from zero of small denominators with the corresponding asymptotics was established. This assessment allowed under certain conditions relative to the set objectives and functions to prove convergence of the constructed series in the class of regular solutions and the stability of the solution.

Keywords: equation of mixed type nonlocal problem, uniqueness criterion, the existence, series, small denominators, stability

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-00421-мол_а
This work was supported by the Russian Foundation for Basic Research (project no. 16–31–00421-mol_a).


DOI: https://doi.org/10.14498/vsgtu1470

Full text: PDF file (674 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.957
MSC: 35M12
Original article submitted 24/I/2016
revision submitted – 13/II/2016

Citation: V. A. Gushchina, “The nonlocal A. A. Desin's problem for an equation of mixed elliptic-hyperbolic type”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:1 (2016), 22–32

Citation in format AMSBIB
\Bibitem{Gus16}
\by V.~A.~Gushchina
\paper The nonlocal A.~A.~Desin's problem for an equation of mixed elliptic-hyperbolic type
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 1
\pages 22--32
\mathnet{http://mi.mathnet.ru/vsgtu1470}
\crossref{https://doi.org/10.14498/vsgtu1470}
\zmath{https://zbmath.org/?q=an:06964469}
\elib{http://elibrary.ru/item.asp?id=26898055}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. A. Kirzhinov, “O reshenii analoga zadachi A. A. Dezina dlya uravneniya smeshannogo tipa vtorogo poryadka metodom funktsii Grina”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2018, no. 3(23), 36–41  mathnet  crossref  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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