On the asymptotic solution of the singularly perturbed boundary value problems posed by Bohé
type: Item
instance of: scholarly article
title: On the asymptotic solution of the singularly perturbed boundary value problems posed by Bohé
zbMATH Open document ID: 0965.34010
author: Robert E. jun. O'Malley
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-07-29T00:00:00Z
review text: The author studies the asymptotic solution to the two-point Dirichlet boundary value problem for the scalar second-order singularly perturbed nonlinear ordinary differential equation \(\varepsilon\ddot x= g(x)f(\dot x)\) on the interval \(0\leq t\leq 1\). The interior shock layer where the solution jumps from nearly \(x(0)\) to nearly \(x(1)\) is considered.
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1423636
zbMATH Keywords: asymptotic solution
zbMATH Keywords: singular perturbation
zbMATH Keywords: boundary value problem
zbMATH Keywords: interior shock layer
reviewed by: Jiaqi Mo
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6641
OpenAlex ID: W2032275377
cites work: Boundary Layer Problems Exhibiting Resonance
cites work: Q3497396
cites work: Free Layers in a Singularly Perturbed Boundary Value Problem
cites work: Free layers and singular jumps in some singularly perturbed boundary value problems with turning points
cites work: The existence of supersensitive boundary-value problems
cites work: The shock location for a class of sensitive boundary value problems
cites work: On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
cites work: Q5544538
cites work: Sauts des Solutions des Équations $\varepsilon \ddot x = f(t,x,\dot x)$
cites work: Nonstandard analysis in practice
cites work: Applications of the Maximum Principle to Singular Perturbation Problems
cites work: Boundary-interior layer interactions in nonlinear singular perturbation theory
cites work: An analytical treatment of the formation of one-dimensional steady shock waves in uniform and diverging ducts
cites work: Q3138728
cites work: Metastable travelling-wave solutions of singularly-perturbed reaction-diffusion equations
cites work: Matched asymptotic expansions. Ideas and techniques
cites work: Q3976483
cites work: Singular perturbation methods for ordinary differential equations
cites work: NAIVE SINGULAR PERTURBATION THEORY
cites work: Q4380780
cites work: On Non‐Linear Ordinary Differential Equations of Boundary Layer Type
cites work: On the exponentially slow motion of a viscous shock
cites work: Q3272002
cites work: Q4151274
DOI: 10.1006/JMAA.1999.6641
description: scientific article; zbMATH DE number 1423636