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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2013, Volume 6, Issue 4, Pages 55–62 (Mi vyuru104)  

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

Mathematical Modelling

Analysis of Solvability for Weak Nonlinear Differential Algebraic Systems

M. A. Perepelitsaa, A. A. Pokutnyib

a Taras Shevchenko National University of Kyiv, Kiev, Ukraine
b Institute of Mathematics NAS, Kiev, Ukraine
Full-text PDF (390 kB) Citations (1)
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Abstract: In this paper we consider the system of differential algebraic equations with a linear part and a small nonlinear term. We refer to such systems as weak nonlinear. Coefficient matrices of the linear part might be rectangular. Additionally, it is assumed that the solution meets some boundary conditions of a general kind. Basic assumption for the linear part is that it can be reduced to canonic form introduced by V. F. Chistyakov. By applying a special technique, analysis of the boundary problem is reduced to mastering of an operator which becomes a compression at a sufficiently small parameter. Under assumptions mentioned, we obtain sufficient and necessary existence conditions for weak nonlinear differential algebraic systems.
Keywords: differential algebraic equations; index; implicit; weakly nonlinear.
Received: 15.08.2013
Document Type: Article
UDC: 517.518
MSC: 65L80
Language: Russian
Citation: M. A. Perepelitsa, A. A. Pokutnyi, “Analysis of Solvability for Weak Nonlinear Differential Algebraic Systems”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:4 (2013), 55–62
Citation in format AMSBIB
\Bibitem{PerPok13}
\by M.~A.~Perepelitsa, A.~A.~Pokutnyi
\paper Analysis of Solvability for Weak Nonlinear Differential Algebraic Systems
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2013
\vol 6
\issue 4
\pages 55--62
\mathnet{http://mi.mathnet.ru/vyuru104}
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  • This publication is cited in the following 1 articles:
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    References:51
    First page:1
     
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