Non-classical boundary layers for fourth-order equations with singular limit solution

Abstract

In this article we study non classical singular perturbation problems involving boundary layers in the interior of the domain. As usual, these problems contain a small parameter which produces, when this parameter approaches zero, classical boundary layers located at the boundary. If we moreover consider a singular source function, we produce also boundary layers inside the domain. Our aim in this article is to study this kind of boundary layers. We consider, here, a model with a fourth-order differential operator, and the open set is a channel to avoid the technicalities due to the curvature of the boundary. Other stationary problems and time dependent problems will be considered elsewhere.