Global asymptotic expansion for anisotropic singularly perturbed elliptic problems

TL;DR

This paper develops a global asymptotic expansion for solutions to anisotropic singularly perturbed elliptic problems, providing insights into their behavior as perturbation parameters tend to zero.

Contribution

It introduces a novel method to obtain a global asymptotic expansion for anisotropic singular perturbations in linear elliptic problems.

Findings

Established a global asymptotic expansion in specific functional spaces

Analyzed the effects of anisotropy on solution behavior

Provided theoretical framework for future numerical methods

Abstract

In this paper, we study some anisotropic singular perturbations for a class of linear elliptic problems. We show a global asymptotic expansion of the solution in certain functional space.