Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 195, Pages 51–56
DOI: https://doi.org/10.36535/0233-6723-2021-195-51-56 (Mi into832) 		 
On the Cauchy problem for the descriptor equation with perturbation in the right-hand side

S. P. Zubovaa, E. V. Raetskayab

a Voronezh State University
b Voronezh State University of Forestry and Technologies named after G.F. Morozov
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DOI: https://doi.org/10.36535/0233-6723-2021-195-51-56
Abstract: We consider the Cauchy problem for a differential equation with a Fredholm operator acting on the derivative whose right-hand side depends on a small parameter. We examine the behavior of solutions as the parameter tends to zero and establish a connection between the sensitivity of solutions to perturbations and the relation between the lengths of some Jordan chains and the orders of the poles of some operators. The conditions for the appearance of boundary layers are determined.
Keywords: descriptor equation, perturbation, boundary layer, Newton diagram.
Bibliographic databases:
Document Type: Article
UDC: 517.25, 517.98
MSC: 34E15, 47A13
Language: Russian
Citation: S. P. Zubova, E. V. Raetskaya, “On the Cauchy problem for the descriptor equation with perturbation in the right-hand side”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 195, VINITI, Moscow, 2021, 51–56
Citation in format AMSBIB
\Bibitem{ZubRae21}
\by S.~P.~Zubova, E.~V.~Raetskaya
\paper On the Cauchy problem for the descriptor equation with perturbation in the right-hand side
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 195
\pages 51--56
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into832}
\crossref{https://doi.org/10.36535/0233-6723-2021-195-51-56}
\elib{https://elibrary.ru/item.asp?id=46664809}
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