On boundary layers for the Burgers equations in a bounded domain

As a simplified model derived from the Navier-Stokes equations, we consider the viscous Burgers equations in a bounded domain with two-point boundary conditions. We investigate the singular behaviors of their solutions uε as the viscosity parameter ε gets smaller. The idea is constructing the asymptotic expansions in the order of the ε and validating the convergence of the expansions to the solutions uε as ε → 0. In this article, we consider the case where sharp transitions occur at the boundaries, i.e. boundary layers, and we fully analyze the convergence at any order of ε using the so-called boundary layer correctors. We also numerically verify the convergences.