A geometric analysis of the Lagerstrom model problem
type: Item
instance of: scholarly article
title: A geometric analysis of the Lagerstrom model problem
zbMATH Open document ID: 1059.34033
author: Peter Szmolyan
author: Nikola Popović
published in: Journal of Differential Equations
publication date: 2004-10-01T00:00:00Z
review text: The paper is devoted to the study of the Langerstrom model which describes the viscous flow past a solid at low Reynolds number. Here, the authors analyze geometrically the corresponding boundary value problem by using methods from the theory of dynamical systems, in particular invariant manifolds. However, this well-developed method is not applicable at points, where the normal hyperbolicity is lost. As an essential part of the dynamics takes place near a line of nonhyperbolic equilibria, a blow-up transformation is introduced to resolve these singularities. This approach leads to a constructive proof of existence and local uniqueness of solutions and to a better understanding of the singular perturbation nature of the problem. In particular, the source of the logarithmic switchback phenomenon is identified.
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 2104513
zbMATH Keywords: singular perturbation
zbMATH Keywords: blow-up method
zbMATH Keywords: invariant manifold
zbMATH Keywords: existence and uniqueness of solutions
MaRDI profile type: Publication
full work available at URL: j.jde.2003.08.004
OpenAlex ID: W2073156822
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DOI: 10.1016/J.JDE.2003.08.004
description: scientific article; zbMATH DE number 2104513