Abstract
One common characteristic of many classical singular perturbation problemsis the occurrence of logarithmic (switchback) terms in the correspondingasymptotic expansions. We discuss two such problems well known to give rise tologarithmic switchback: first, Lagerstrom's equation, a model related tothe asymptotic treatment of low Reynolds number flow from fluidmechanics, and second, the Evans function approach to the stability ofdegenerate shock waves in (scalar) reaction-diffusion equations. We showhow asymptotic expansions for these two problems can be obtained by meansof methods from dynamical systems theory as well as of the blow-uptechnique. We identify the structure of these expansions anddemonstrate that the occurrence of the logarithmic switchback terms thereinis in fact caused by a resonance phenomenon.
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