Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2017, Volume 23, Number 2, Pages 42–66
DOI: https://doi.org/10.21538/0134-4889-2017-23-2-42-66 (Mi timm1411) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (345 kB) Citations (2)
References:
PDF
HTML
DOI: https://doi.org/10.21538/0134-4889-2017-23-2-42-66
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.
Received: 01.02.2017
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 93C70, 49N05, 34E05, 34E10, 34K26, 34K28, 35K15, 35K59, 35C20
Language: Russian
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}
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:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Instituta Matematiki i Mekhaniki UrO RAN
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025