Rigorous asymptotic expansions for Lagerstrom’s model equation—A geometric approach, Nonlinear Anal. 59

Abstract. The present work is a continuation of the geometric singular per-turbation analysis of the Lagerstrom model problem which was commenced in [PS04]. 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. 1