Rigorous asymptotic expansions for Lagerstrom's model equation - a geometric approach

N Popovic*, P Smolyan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The present work is a continuation of the geometric singular perturbation analysis of the Lagerstrom model problem which was commenced in J. Differential Equations (199 (2) (2004) 290-325). We establish the same framework here, reinterpreting Lagerstrom's equation as a dynamical system which is subsequently analyzed by means of methods from dynamical systems theory as well as of the blow-up technique. We show how rigorous asymptotic expansions for the Lagerstrom problem can be obtained using geometric methods, thereby establishing a connection to the method of matched asymptotic expansions. We explain the structure of these expansions and demonstrate that the occurrence of the well-known logarithmic (switchback) terms therein is caused by a resonance phenomenon. (C) 2004 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)531-565
Number of pages35
Journal Nonlinear Analysis: Theory, Methods and Applications
Volume59
Issue number4
DOIs
Publication statusPublished - Nov 2004

Keywords / Materials (for Non-textual outputs)

  • singular perturbations
  • asymptotic expansions
  • switchback
  • SINGULAR PERTURBATION-THEORY
  • SMALL REYNOLDS NUMBERS
  • CIRCULAR CYLINDER
  • FLOW

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