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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2014, Issue 1(34), Pages 9–18
DOI: https://doi.org/10.14498/vsgtu1258
(Mi vsgtu1258)
 

Differential Equations

Models of Multiparameter Bifurcation Problems for the Fourth Order Ordinary Differential Equations

T. E. Badokina

Ogarev Mordovia State University, Saransk, 430005, Russian Federation (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: We consider the problem of computing the bifurcating solutions of nonlinear eigenvalue problem for an ordinary differential equation of the fourth order, describing the divergence of the elongated plate in a supersonic gas flow, compressing (extending) by external boundary stresses on the example of the boundary conditions (the left edge is rigidly fixed, the right one is free). Calculations are based on the representation of the bifurcation parameter using the roots of the characteristic equation of the corresponding linearized operator. This representation allows one to investigate the problem in a precise statement and to find the critical bifurcation surfaces and curves in the neighborhood of which the asymptotics of branching solutions is being constructed in the form of convergent series in the small parameters. The greatest difficulties arise in the study of the linearized spectral problem. Its Fredholmness is proved by constructing the corresponding Green's function and for this type of problems it is performed for the first time.
Keywords: supersonic gas flow, buckling, aeroelasticity, bifurcation, branching equation.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.В37.21.0373
This work was supported by Federal Target Program “Research and scientific-pedagogical personnel of innovative Russia in 2009-2013”, the agreement 14.В37.21.0373 on 14/11/2012.
Original article submitted 03/IX/2013
revision submitted – 24/I/2014
Bibliographic databases:
Document Type: Article
UDC: 517.988.67
MSC: 34B08, 58E07
Language: Russian
Citation: T. E. Badokina, “Models of Multiparameter Bifurcation Problems for the Fourth Order Ordinary Differential Equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(34) (2014), 9–18
Citation in format AMSBIB
\Bibitem{Bad14}
\by T.~E.~Badokina
\paper Models of Multiparameter Bifurcation Problems for~the~Fourth Order Ordinary Differential Equations
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 1(34)
\pages 9--18
\mathnet{http://mi.mathnet.ru/vsgtu1258}
\crossref{https://doi.org/10.14498/vsgtu1258}
\zmath{https://zbmath.org/?q=an:06968820}
\elib{https://elibrary.ru/item.asp?id=22813955}
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    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Abstract page:469
    Full-text PDF :233
    References:88
     
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