Singular perturbation problems in a general smooth domain

Article type: Research Article

Authors: Gie, Gung-Min

Affiliations: The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Bloomington, IN 47405, USA. E-mail: gugie@indiana.edu

Abstract: The goal of this article is to study the boundary layer of a reaction-diffusion equation with a small viscosity in a general (curved), bounded and smooth domain in Rn, n≥2. To the best of our knowledge, the classical expansion in the case of a bounded interval or of a channel is not valid for a general domain. Using the techniques of differential geometry, a new asymptotic expansion proposed in this article recovers the optimal convergence rate of the remainder at all orders.

Keywords: boundary layers, singular perturbation analysis, reaction–diffusion, curvilinear coordinates

DOI: 10.3233/ASY-2009-0922

Journal: Asymptotic Analysis, vol. 62, no. 3-4, pp. 227-249, 2009