Asymptotic expansion of the solution of a mixed Dirichlet–Ventcel problem with a small parameter

Abstract

A mixed Dirichlet–Ventcel problem with a small parameter in a polygonal domain of the plane is considered. Since the limit problem is a mixed Dirichlet–Neumann problem, we are in presence of a singular perturbed problem. We give the full asymptotic of the solution of the Dirichlet–Ventcel problem with the help of outer terms and boundary layer terms. Here the main difficulty relies on the singular behaviour of the solutions near the corner points where the boundary conditions change, so that the boundary layer terms are corner layer terms.