Asymptotic Behavior and Stability of a Stationary Boundary-Layer Solution to a Partially Dissipative System of Equations

Abstract

A boundary value problem for a singularly perturbed partially dissipative system of two ordinary differential equations of the second and first order, respectively, is considered. An asymptotic expansion of its boundary-layer solution in a small parameter is constructed and justified. This solution is a stationary solution of the corresponding evolution system of equations with partial derivatives. The asymptotic stability of a stationary boundary-layer solution is proved, and its local basin of attraction is found.