On a degenerate elliptic singular perturbation

Article type: Research Article

Authors: Didelot, S. | Frank, L.S. | Maigrot, L.

Affiliations: Université de Reims, Champagne-Ardenne U.F.R. Sciences, Départment de Mathématiques, Moulin de la Housse, B.P. 1039, 51687 Reims Cedex 2, France

Note: [] Corresponding author.

Abstract: The method of constructive reduction of elliptic and coercive singular perturbations to regular ones, developed in [2–7] is applied to so-called bisingular singularly perturbed boundary value problems (see, for instance, [8]). The reduction procedure allows to derive asymptotic formulae for the solutions of these problems, without going through the matching of different locally formally derived asymptotic expansions (see [8,9,11]). The advantage of using the reduction procedure consists not only in the globality of asymptotic formulae thus obtained, but also in a simple proof of their asymptotic convergence as a direct consequence of the central reduction to regular perturbations result.

DOI: 10.3233/ASY-1997-15202

Journal: Asymptotic Analysis, vol. 15, no. 2, pp. 151-181, 1997