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Mathematics of the USSR-Izvestiya, 1990, Volume 34, Issue 2, Pages 261–279
DOI: https://doi.org/10.1070/IM1990v034n02ABEH000629
(Mi im1240)
 

This article is cited in 8 scientific papers (total in 10 papers)

On the asymptotics of the solution of a problem with a small parameter

A. M. Il'in
References:
Abstract: The problem $\partial_tu+\partial_x\varphi(u)=\varepsilon\partial_x^2u$, $u(x,t_0)=\psi(x)$, is considered, where $\varphi,\psi\in C^\infty$, $\varphi''(u)>0$, $0\leqslant\varepsilon\ll1$. It is assumed that for $\varepsilon=0$ the problem has a generalized solution with one smooth line of discontinuity, so that this line, modeling a shock wave, appears within the strip $\Omega=\{t_0\leqslant t\leqslant T\}$. The asymptotics of a solution, uniform in $\Omega$ up to any degree in $\varepsilon$, is constructed and justified.
Bibliography: 18 titles.
Received: 24.03.1986
Revised: 17.01.1988
Bibliographic databases:
UDC: 517.956
MSC: Primary 35K55, 35B25, 35C20; Secondary 76L05
Language: English
Original paper language: Russian
Citation: A. M. Il'in, “On the asymptotics of the solution of a problem with a small parameter”, Math. USSR-Izv., 34:2 (1990), 261–279
Citation in format AMSBIB
\Bibitem{Ili89}
\by A.~M.~Il'in
\paper On the asymptotics of the solution of a~problem with a~small parameter
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 2
\pages 261--279
\mathnet{http://mi.mathnet.ru//eng/im1240}
\crossref{https://doi.org/10.1070/IM1990v034n02ABEH000629}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=998296}
\zmath{https://zbmath.org/?q=an:0703.35012}
Linking options:
  • https://www.mathnet.ru/eng/im1240
  • https://doi.org/10.1070/IM1990v034n02ABEH000629
  • https://www.mathnet.ru/eng/im/v53/i2/p258
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:491
    Russian version PDF:139
    English version PDF:15
    References:73
    First page:3
     
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