Abstract
Lagerstrom's model problem is a classical singular perturbation problem which was introduced to illustrate the ideas and subtleties involved in the analysis of viscous flow past a solid at low Reynolds number by the method of matched asymptotic expansions. In this paper the corresponding boundary value problem is analyzed geometrically by using methods from the theory of dynamical systems, in particular invariant manifold theory. As an essential part of the dynamics takes place near a line of non-hyperbolic 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. (C) 2003 Elsevier Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 290-325 |
Number of pages | 36 |
Journal | Journal of Differential Equations |
Volume | 199 |
Issue number | 2 |
DOIs | |
Publication status | Published - 20 May 2004 |
Keywords / Materials (for Non-textual outputs)
- singular perturbations
- invariant manifolds
- blow-up
- LOW-REYNOLDS-NUMBER
- SINGULAR PERTURBATION-THEORY
- CIRCULAR CYLINDER
- VISCOUS-FLOW
- EXPANSIONS
- EQUATION
- POINTS