ISSN:
1573-2754
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Mathematics
,
Physics
Notes:
Abstract In this paper we study initial value problems on the infinite interval: (1.1) $$\left. {\begin{array}{*{20}c} {\frac{{dx}}{{dt}} = f(t, x, y; \varepsilon ),} & {x(0, \varepsilon ) = \xi (\varepsilon )} \\ {e\frac{{dy}}{{dt}} = g(t, x, y; \varepsilon ),} & {y(0, \varepsilon ) = \eta (\varepsilon )} \\ \end{array} } \right\}$$ where x, ƒ∈E m, y, g∈En,ε are real small positive parameters,0ť+∞.On condition that g y (t) is nonsingular and under other assumptions, we have proved that there are serial (k+m*)-dimensional manifolds {SR(ε)}∈Em+n such that (1.1) degenerates regularly provided (ξ(ε), η(ε))∈SR(ε).Besides, the R-order asymptotic expansions of solutions are constructed, and their errors are estimated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02017979
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