Regularized asymptotic solutions to singularly perturbed problems in a critical case
type: Item
instance of: scholarly article
title: Regularized asymptotic solutions to singularly perturbed problems in a critical case
zbMATH Open document ID: 0830.34046
published in: Russian Mathematics
publication date: 1995-09-17T00:00:00Z
review text: The author constructs regularized asymptotic solutions to the singularly perturbed problem \(\varepsilon dy/dt= Ay+ f(y)+ \varepsilon \Phi(y, t)\), \(y(0, \varepsilon)= y^0\), \(t\in [0, T]\), where \(y\in \mathbb{R}^2\), \(f(0)= 0\), \(fy'(0)= 0\), \(\varepsilon> 0\) is a small parameter, and the \(2\times 2\) matrix \(A\) has the purely imaginary eigenvalues \(\lambda_{1, 2}= \pm i\omega\) \((\omega> 0)\). The construction is based on a normal form algorithm developed by \textit{Yu. A. Gubin} and the author in [Differ. Equations 20, 665-674 (1984); translation from Differ. Uravn. 20, 930-941 (1984; Zbl 0561.34039)].
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 794584
zbMATH Keywords: regularized asymptotic solutions
zbMATH Keywords: singularly perturbed problem
zbMATH Keywords: normal form algorithm
author: V. F. Safonov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 794584