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Sbornik: Mathematics, 2007, Volume 198, Issue 9, Pages 1299–1324
DOI: https://doi.org/10.1070/SM2007v198n09ABEH003884 (Mi sm3822) 		 
This article is cited in 1 scientific paper (total in 3 paper)

Asymptotic behaviour of a special solution of Abel's equation relating to a cusp catastrophe. II. Large values of the parameter $t$

A. M. Il'ina, B. I. Suleimanovb

a Chelyabinsk State University
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
English version PDF (435 kB) Citations (3) Russian version article
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DOI: https://doi.org/10.1070/SM2007v198n09ABEH003884
Abstract: An asymptotic formula as $t\to\infty$ for the solution of the ordinary differential Abel's equation of the first kind $u'_x+u^3-tu-x=0$, which is uniform in the $x$-variable, is constructed and substantiated.
Bibliography: 13 titles.
Received: 18.12.2006
Bibliographic databases:
UDC: 517.928
MSC: Primary 34E05; Secondary 58K35
Language: English
Original paper language: Russian
Citation: A. M. Il'in, B. I. Suleimanov, “Asymptotic behaviour of a special solution of Abel's equation relating to a cusp catastrophe. II. Large values of the parameter $t$”, Sb. Math., 198:9 (2007), 1299–1324
Citation in format AMSBIB
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\by A.~M.~Il'in, B.~I.~Suleimanov
\paper Asymptotic behaviour of a~special solution of Abel's equation relating to a~cusp catastrophe.
II.~Large values of the parameter~$t$
\jour Sb. Math.
\yr 2007
\vol 198
\issue 9
\pages 1299--1324
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  • https://doi.org/10.1070/SM2007v198n09ABEH003884
  • https://www.mathnet.ru/eng/sm/v198/i9/p81
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