自治ODE爆破解的多阶渐近展开 I——方法与论证
经典分析与常微分方程
2022-12-01 v2
摘要
本文针对自治常微分方程（ODEs）的爆破解，给出一种在爆破点附近计算其多阶渐近展开的系统方法。在一类向量场爆破解主项特定形式下，我们提取出决定渐近展开中所有可能阶数的代数对象。最后汇集了计算爆破解具体多阶渐近展开的若干实例。
引用
@article{arxiv.2211.06865,
title = {Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. I -- Method and Justification},
author = {Taisei Asai and Hisatoshi Kodani and Kaname Matsue and Hiroyuki Ochiai and Takiko Sasaki},
journal= {arXiv preprint arXiv:2211.06865},
year = {2022}
}
备注
78 pages. This is the first part in the present subject. Part II entitled "Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II - Dynamical Correspondence" is also uploaded (arXiv:2211.06868). In v2, unclear expressions are corrected