Singular perturbation problems in a general smooth domain

Abstract

The goal of this article is to study the boundary layer of a reaction-diffusion equation with a small viscosity in a general (curved), bounded and smooth domain in Rⁿ, n≥2. To the best of our knowledge, the classical expansion in the case of a bounded interval or of a channel is not valid for a general domain. Using the techniques of differential geometry, a new asymptotic expansion proposed in this article recovers the optimal convergence rate of the remainder at all orders.