Publications in Scientific Journals:

N. Popovic, P. Szmolyan:
"A geometric analysis of the lagerstrom model problem";
Journal of Differential Equations, 199 (2004), 290 - 325.

English 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.

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