Analytic regularity for a singularly perturbed reaction-convection-diffusion boundary value problem with two small parameters

TL;DR

This paper analyzes a reaction-convection-diffusion boundary value problem with two small parameters, establishing explicit regularity bounds and a decomposition into smooth and boundary layer parts, providing detailed derivative estimates.

Contribution

It provides explicit differentiability bounds and a solution decomposition for a singularly perturbed problem with two small parameters, advancing understanding of its regularity structure.

Findings

Derived classical differentiability bounds explicit in perturbation parameters

Decomposed solution into smooth, boundary layers, and negligible remainder

Obtained derivative estimates for each component of the solution

Abstract

We consider a second order, two-point, singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and we obtain regularity results for its solution. First we establish classical differentiability bounds that are explicit in the order of differentiation and the singular perturbation parameters. Next, for small values of these parameters we show that the solution can be decomposed into a smooth part, boundary layers at the two endpoints and a negligible remainder. Derivative estimates are obtained for each component of the solution, which again are explicit in the differentiation order and the singular perturbation parameters.