无穷区域上非线性向量方程初值问题的解的渐近性质
Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval
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摘要: 本文研究无穷域上的初值问题:其中x,f∈Em,y,g∈En,实的小参数ε>0,0≤t<+∞,在gr(t)是非奇异的和其它适当的假设下,证明了存在一系列k+m*维流形{SR(ε)}∈Em+n,使得如果(ξ(ε),η(ε))∈SR(ε),方程(1.1)是正则退化的,并作出了解的R阶渐近展开式及其余项估计。Abstract: In this paper we study initial value problems on the infinite interval: where x, f∈Em, y, g∈En,εare real small positive parameters,0≤t<+∞. On condition that gy(t) is nonsingular and under other assumptions, we have proved that there areserial (k+m*)-dimensionalmanifolds {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.
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