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 <nobr>$t$</nobr>”, Mat. Sb., 2007, Volume 198, Number 9,Pages <nobr>81

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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'in^a, B. I. Suleimanov^b

^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.

UDC: 517.928

MSC: Primary 34E05; Secondary 58K35

Received: 18.12.2006

DOI: 10.4213/sm3822