A parabolic singular perturbation problem with an internal layer

Article type: Research Article

Authors: Grasman, Johan^; | Shih, Shagi‐Di

Affiliations: Group Mathematical and Statistical Methods, Wageningen University and Research Centre, Postbus 100, 6700 AC Wageningen, The Netherlands E‐mail: [email protected] | Department of Mathematics, University of Wyoming, P.O. Box 3036, Laramie, WY 82071, USA E‐mail: [email protected]

Note: [] Corresponding author.

Abstract: A method is presented to approximate with singular perturbation methods a parabolic differential equation for the quarter plane with a discontinuity at the corner. This discontinuity gives rise to an internal layer. It is necessary to match the local solution in this layer with the one in a corner layer as otherwise terms in the internal layer solution remain unnoticed. The problem is explained using the exact solution of a special case. The asymptotic solution is proved to approximate the exact solution in the general case using the maximum principle for parabolic differential equations.

Keywords: singular perturbation, asymptotic approximation, internal layer, corner layer, asymptotic matching, maximum principle

Journal: Asymptotic Analysis, vol. 38, no. 3-4, pp. 309-318, 2004