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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2015, Volume 19, Number 4, Pages 634–649
DOI: https://doi.org/10.14498/vsgtu1384 (Mi vsgtu1384) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Differential Equations and Mathematical Physics

The Dirichlet problem for mixed type equation with two lines of degeneracy in a rectangular area

A. A. Gimaltdinova

Sterlitamak branch of Bashkir State University, Sterlitamak, 453103, Russian Federation
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(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu1384
Abstract: We study the first boundary value problem for the elliptic-hyperbolic type equation with two perpendicular lines of change of type and spectral parameter. We prove the existence and uniqueness of the solution. In the proof of the uniqueness of solution we use the completeness of biorthogonal system in space $ L_2$. When building a solution as the sum of a series there is a problem of small denominators. We obtained estimates of the denominators of the separation from zero.
Keywords: mixed type equation, Dirichlet problem, uniqueness, existence of a solution, spectral method.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-97003-р_Поволжье_а
This work has been supported by the Russian Foundation for Basic Research (project no. 14–01–97003-r_Povolzh'e_a).
Original article submitted 19/XII/2014
revision submitted – 20/II/2015
Bibliographic databases:
Document Type: Article
UDC: 517.956.6
MSC: 35M12
Language: Russian
Citation: A. A. Gimaltdinova, “The Dirichlet problem for mixed type equation with two lines of degeneracy in a rectangular area”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:4 (2015), 634–649
Citation in format AMSBIB
\Bibitem{Gim15}
\by A.~A.~Gimaltdinova
\paper The Dirichlet problem for mixed type equation with two lines of degeneracy in a rectangular area
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 4
\pages 634--649
\mathnet{http://mi.mathnet.ru/vsgtu1384}
\crossref{https://doi.org/10.14498/vsgtu1384}
\zmath{https://zbmath.org/?q=an:06969183}
\elib{https://elibrary.ru/item.asp?id=25687492}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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