Geodesic
On global in time solutions for differential-algebraic equations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 3, pp. 33-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate differential-algebraic equations arising in mathematical models that describe some radio-technical devises. A class of differential-algebraic equations is described, for which necessary and sufficient conditions for global in time existence of solutions are proved. As well as in many papers where sufficient conditions for such equations are obtained, we reduce them to ordinary differential equations and then apply the necessary and sufficient conditions for the latter. We deal with the systems whose matrix pencil is regular and (for simplicity) the characteristic polynomial satisfies the rank-degree condition. We also require some additional conditions that allow us to reduce the differential-algebraic system to ordinary differential one.
Keywords: differential-algebraic equation; global existence of solution; proper function; complete Riemannian metric. 
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Yu. E. Gliklikh. On global in time solutions for differential-algebraic equations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 3, pp. 33-39. http://geodesic.mathdoc.fr/item/VYURU_2014_7_3_a2/

[1] Shestakov A. L., Sviridyuk G. A., “A New Approach to Measurement of Dynamically Perturbed Signals”, Bulletin of the South Ural State University. Series Mathematical Modelling, Programming Computer Software, 2010, no. 16 (192), issue 5, 116–120 (in Russian) | Zbl

[2] Shestakov A. L., Sviridyuk G. A., “Optimal Measurement of Dynamically Distorted Signals”, Bulletin of the South Ural State University. Series Mathematical Modelling, Programming Computer Software, 2011, no. 17 (234), issue 8, 70–75 | Zbl

[3] Filipkovskaya M. S., “On Conditions of Global Solvability of Differential-Algebraic Equations”, Materials of International Conference “S. G. Krein Voronezh Winter Mathematical School–2014”, Voronezh State University, Voronezh, 2014, 362–372 (in Russian)

[4] Rutkas A. G., Filipkovskaya M. S., “Prolongation of Solutions of a Certain Class of Differential-Algebraic Equations”, Zhurnal obchislyuvalnoyi ta prikladnoyi matematyky, 2013, no. 1, 135–145 (in Russian)

[5] Filipkovskaya M. S., “Prolongation of Solutions for a Certain Class of Differential-Algebraic Equations and Applications to non-linear Radio-Engineering”, Visnyk of Kharkov National University. Series Mathematical Modelling, Informational Technologies and Automatic Control Systems, 2012, no. 1015, issue 19, 306–319 (in Russian)

[6] Gliklikh Yu. E., “On Non-Local Prolongation Conditions for Integral Curves of Vector Fields”, Differential Equations, 12:4 (1977), 743–744 (in Russian)

[7] Gliklikh Yu. E., “Necessary and Sufficient Conditions for Global in Time Existence of Solutions of Ordinary, Stochastic, and Parabolic Differential Equations”, Abstract and Applied Analysis, 2006, 39786, 1–17 | MR

[8] Gliklikh Yu. E., Global and Stochastic Analysis with Applications to Mathematical Physics, Springer-Verlag, London, 2011, 460 pp. | DOI | MR | Zbl

[9] Chistyakov V. F., Shcheglova A. A., Selected Chapters of Differential Algebraic Equations Theory, Nauka, Novosibirsk, 2003, 320 pp. | MR | Zbl

[10] Gantmakher F. R., Theory of Matrices, Fizmatlit, M., 1967, 575 pp.