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Mat. Sb., 2007, Volume 198, Number 9, Pages 81–106 (Mi msb3822)  

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

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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm3822

Full text: PDF file (674 kB)
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English version:
Sbornik: Mathematics, 2007, 198:9, 1299–1324

Bibliographic databases:

UDC: 517.928
MSC: Primary 34E05; Secondary 58K35
Received: 18.12.2006

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 $t$”, Mat. Sb., 198:9 (2007), 81–106; Sb. Math., 198:9 (2007), 1299–1324

Citation in format AMSBIB
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