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

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.