Asymptotics of the Solution of a System of Singularly Perturbed Equations in the Case of a Multiple Root of the Degenerate Equation

摘要

We construct and justify the asymptotics of the solution of a boundary value problem for a singularly perturbed system of two second-order ordinary differential equations that contain distinct powers of a small parameter multiplying second-order derivatives for the case of a multiple root of the degenerate equation. The root multiplicity results in changes in the structure of the asymptotics of the boundary layer solution as compared with the case of a simple root, in particular, in changes in the scale of the boundary layer variables.