Abstract

Joining of Approximate Asymptotic Groups for Some Model Examples

R.Khabibullin, I.B.Vasil'ev (Department of Mathematics, Ufa State Aviation Technical University,Ufa, Russia)

e-mail: baikov@math.ugatu.ac.ru.

We have considered some ordinary differential equations with a small parameter by the higher derivatives (the van der Pol equation and the Stokes-Oseen problem). There are singular boundary problems based on such equations. The group properties of these problems are investigated using the method of approximate group analysis. Here we try to apply the method of joining of asymptotic expantions in the theory of approximate group analysis. For the considered problem we offer an algorithm of joining asymptotic expantions of approximate groups. Such approach provides the obtaining of uniformly suitable invariant solutions for these problems.

Section : 12