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 Trudy Inst. Mat. i Mekh. UrO RAN, 2017, Volume 23, Number 2, Pages 42–66 (Mi timm1411)

The Yekaterinburg heritage of Arlen Mikhailovich Il'in

A. R. Danilinab, S. V. Zakharova, O. O. Kovrizhnykhab, E. F. Lelikovaba, I. V. Pershina, O. Yu. Khachayb

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: The main problems formulated by A.M.Il'in and solved by his disciples working now in Yekaterinburg are considered. These problems are related to the method of matched asymptotic expansions used for finding asymptotic solutions of equations with a singular dependence on a small parameter. In addition to boundary value problems for equations of mathematical physics, we consider systems of nonlinear equations and systems of linear equations depending on two small parameters. We also consider problems of finding asymptotic expansions for fundamental solutions of parabolic equations and optimal control problems depending on a small parameter.

Keywords: singularly perturbed problems, asymptotic expansions, small parameter, method of matched asymptotic expansions, optimal control.

DOI: https://doi.org/10.21538/0134-4889-2017-23-2-42-66

Full text: PDF file (345 kB)
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Bibliographic databases:

UDC: 517.977
MSC: 93C70, 49N05, 34E05, 34E10, 34K26, 34K28, 35K15, 35K59, 35C20

Citation: A. R. Danilin, S. V. Zakharov, O. O. Kovrizhnykh, E. F. Lelikova, I. V. Pershin, O. Yu. Khachay, “The Yekaterinburg heritage of Arlen Mikhailovich Il'in”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 2, 2017, 42–66

Citation in format AMSBIB
\Bibitem{DanZakKov17} \by A.~R.~Danilin, S.~V.~Zakharov, O.~O.~Kovrizhnykh, E.~F.~Lelikova, I.~V.~Pershin, O.~Yu.~Khachay \paper The Yekaterinburg heritage of Arlen Mikhailovich Il'in \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2017 \vol 23 \issue 2 \pages 42--66 \mathnet{http://mi.mathnet.ru/timm1411} \crossref{https://doi.org/10.21538/0134-4889-2017-23-2-42-66} \elib{https://elibrary.ru/item.asp?id=29295249}