Small exponent asymptotics. (English) Zbl 0955.74021
Summary: We study the surprisingly complicated asymptotic character of a simple first-order differential equation, which involves a term with a low exponent of the dependent variable. While numerical solutions and straightforward asymptotic expansions indicate a clearly defined boundary layer type transition, we find that the correct asymptotic structure involves a ‘hidden’ boundary layer, and that a straightforward approach cannot discern this.
MSC:
74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |
35B40 | Asymptotic behavior of solutions to PDEs |
86A40 | Glaciology |