Analog of the Method of Boundary Layer Function for the Solution of the Lighthill’s Model Equation with the Regular Singular Point

The possibility of application of the boundary layer function for constructing the asymptotic solution of the singulary perturbed of Lighthill model equation in the case when corresponding not perturbed equation have the pole of the entire order on the regular singular point is proved. Earlier asymptotic of this problem was constructed by the method of uniformization and structural matching. The relations between the methods of the boundary layer function, uniformization and structural matching are analyzed.