On the Formulation of Boundary Layer Functions

In this study, we consider the behavior of solutions of a singularly perturbed integro-differential boundary value problem with an initial jump in the boundary layers. The functions describing the asymptotics in the boundary layer are defined as solutions of third-order differential problems with initial conditions. Furthermore, an example is given to illustrate the results obtained in the construction of the asymptotic expansion of the solution. The purpose of this study is to describe the properties of boundary layer functions for analyzing the influence of a small parameter.