A singularly perturbed system of parabolic equations

TL;DR

This paper develops the asymptotic analysis of solutions to singularly perturbed parabolic systems, especially when the limit equation exhibits a regular singularity, incorporating boundary layer functions.

Contribution

It introduces a method to construct asymptotics for singularly perturbed parabolic systems with regular singularities in the limit equation.

Findings

Asymptotic solutions include boundary layer functions.

Analysis handles regular singularities in the limit equation.

Provides a framework for asymptotic behavior as perturbation parameter tends to zero.

Abstract

The work is devoted to the construction of the asymptotic behavior of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends to zero. The asymptotics of the solution of such problems contains boundary layer functions.