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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/timm1411
https://www.mathnet.ru/eng/timm/v23/i2/p42
This publication is cited in the following 2 articles:
G. A. Kurina, N. T. Hoai, “Zero-Order Asymptotics for the Solution of One Type of Singularly Perturbed Linear–Quadratic Control Problems in the Critical Case”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S154–S169
G. A. Kurina, M. A. Kalashnikova, “Singularly perturbed problems with multi-tempo fast variables”, Autom. Remote Control, 83:11 (2022), 1679–1723
Citation in format AMSBIB
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