An elliptic singularly perturbed problem with two parameters I: Solution decomposition

Abstract

In this paper we consider a singularly perturbed elliptic problem with two small parameters posed on the unit square. Its solution may have exponential, parabolic and corner layers. We give a decomposition of the solution into regular and layer components and derive pointwise bounds on the components and their derivatives. The estimates are obtained by the analysis of appropriate problems on unbounded domains. © 2006 Elsevier B.V. All rights reserved.