Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. I -- Method and Justification
Classical Analysis and ODEs
2022-12-01 v2
Abstract
In this paper, we provide a systematic methodology for calculating multi-order asymptotic expansion of blow-up solutions near blow-up for autonomous ordinary differential equations (ODEs). Under the specific form of the principal term of blow-up solutions for a class of vector fields, we extract algebraic objects determining all possible orders in the asymptotic expansions. Examples for calculating concrete multi-order asymptotic expansions of blow-up solutions are finally collected.
Cite
@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}
}
Comments
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