Implicit differential equations with impasse singularities and singular perturbation problems
type: Item
instance of: scholarly article
title: Implicit differential equations with impasse singularities and singular perturbation problems
zbMATH Open document ID: 1258.34021
author: Pedro T. Cardin
author: Paulo R. da Silva
author: Marco A. Teixeira
published in: Israel Journal of Mathematics
publication date: 2012-11-13T00:00:00Z
review text: The authors study quasi-linear autonomous implicit ordinary differential equations (or shortly constrained systems) with an impasse manifold of codimension \(1\). The main results of the article are two theorems. The first one relates the orbits of a one-parameter family of constrained systems with those of a singular perturbation problem. The second one adapts the invariant manifold theorem of Fenichel to constrained systems. Finally, the authors study the case where the impasse surface is not regular. They show that under two hypotheses, a polar blowup leads to an equivalent constrained system with a regular impasse surface.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C45
zbMATH DE Number: 6105474
zbMATH Keywords: implicit differential equation
zbMATH Keywords: constrained system
zbMATH Keywords: singular perturbations
zbMATH Keywords: singularity
zbMATH Keywords: impasse point
zbMATH Keywords: invariant manifold
MaRDI profile type: Publication
full work available at URL: s11856-011-0169-3
OpenAlex ID: W2071350362
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DOI: 10.1007/S11856-011-0169-3
description: scientific article; zbMATH DE number 6105474