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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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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2013, Issue 3(32), Pages 29–45
DOI: https://doi.org/10.14498/vsgtu1220 (Mi vsgtu1220) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Differential Equations

Boundary value problem for mixed type equation of the third order with periodic conditions

K. B. Sabitova, G. Yu. Udalovab

a Institute of Applied Research, Sterlitamak, Russia, 453103
b Samara State University of Architecture and Construction, Samara, Russia, 443100
Full-text PDF (646 kB) Citations (4)
(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu1220
Abstract: The problem for the equation of the mixed elliptic-hyperbolic type with nonlocal boundary conditions is viewed. This problem is reduced to the inverse problem for elliptic-hyperbolic equation with unknown right-hand parts. The criterion of the uniqueness is established. The explicit solution is constructed as the sum of orthogonal trigonometric series of the one-dimensional spectral problem eigenfunctions. The argumentation of the series convergence under some restrictions is given. The stability of the solution by the boundary functions is proved.
Keywords: equations of the mixed type of third order, direct and inverse problems, spectral method, uniqueness, existense, stability.
Original article submitted 08/IV/2013
revision submitted – 20/VII/2013
Bibliographic databases:
Document Type: Article
UDC: 517.956.6
MSC: Primary 35M12; Secondary 35M10, 35A02
Language: Russian
Citation: K. B. Sabitov, G. Yu. Udalova, “Boundary value problem for mixed type equation of the third order with periodic conditions”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(32) (2013), 29–45
Citation in format AMSBIB
\Bibitem{SabUda13}
\by K.~B.~Sabitov, G.~Yu.~Udalova
\paper Boundary value problem for mixed type equation of the third order with periodic conditions
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 3(32)
\pages 29--45
\mathnet{http://mi.mathnet.ru/vsgtu1220}
\crossref{https://doi.org/10.14498/vsgtu1220}
\zmath{https://zbmath.org/?q=an:06968783}
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  • https://www.mathnet.ru/eng/vsgtu/v132/p29
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Full-text PDF :390
    References:78
    First page:4
     
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