Asymptotic expansion of periodic solutions for a singular perturbation problem including nonlinear dynamical system with two boundary layers
type: Item
instance of: scholarly article
title: Asymptotic expansion of periodic solutions for a singular perturbation problem including nonlinear dynamical system with two boundary layers
zbMATH Open document ID: 1080.34024
author: Yanyan Li
published in: Southeast Asian Bulletin of Mathematics
publication date: 2004-11-01T00:00:00Z
review text: A singularly perturbed problem in the form of two first-order nonlinear differential equations, with periodic boundary conditions, one including a small parameter, on the basic interval \((a, w)\) is considered. The authors are looking for a periodic solution as a sum of an outer and two inner solutions in the form of asymptotic expansions. These asymptotic expansions are obtained for both outer and inner solutions by solving three systems of \(N+ 1\) algebraic and three systems of \(N+ 1\) first-order differential equations, where \(N\) is the degree of truncated asymptotic series. The unknown constants in these solutions are calculated from the periodic and matching conditions which give a system of \(6(N+ 1)\) equations that have to be solved step by step. Remark of the reviewer: The language used hinders the understanding.
reviewed by: Vojislav Marić
Mathematics Subject Classification ID: 34C26
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 2113342
zbMATH Keywords: singular perturbation
zbMATH Keywords: boundary layer
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: periodic conditions
MaRDI profile type: Publication
Recommended article: Q3831294
Recommended article: Q3808477
Recommended article: Asymptotic expansion of solutions to the periodic problem for a non-linear Sobolev-type equation
Recommended article: Asymptotic expansions of the period solutions of nonlinear evolution equations
Recommended article: Q3411119
Recommended article: Q4278786
Recommended article: Q4326892
Recommended article: Asymptotics of solutions of a time-periodic boundary-value problem for a singularly perturbed nonlinear parabolic equation with rapidly oscillating coefficients
Recommended article: Asymptotic behavior of $T$-periodic solutions of singularly perturbed second-order differential equation
Recommended article: Asymptotic Expansion for Layer Solutions of a Singularly Perturbed Reaction-Diffusion System
description: scientific article; zbMATH DE number 2113342