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Zeitschriftenartikel:

N. Popovic, P. Szmolyan:
"Rigorous asymptotic expansions for Lagerstrom's model equation - a geometric approach";
Nonlinear Analysis: Theory, Methods & Applcations, 59 (2004), S. 531 - 565.



Kurzfassung englisch:
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.


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