A singularly perturbed convection–diffusion problem in a half-plane

Abstract

A singularly perturbed convection–diffusion equation with constant coefficients is considered in a half plane, with Dirichlet boundary conditions. The boundary function has a specified degree of regularity except for a jump discontinuity, or jump discontinuity in a derivative of specified order, at a point. Precise pointwise bounds for the derivatives of the solution are obtained. The bounds show both the strength of the interior layer emanating from the point of discontinuity and the blowup of the derivatives resulting from the discontinuity, and make precise the dependence of the derivatives on the singular perturbation parameter.

Keywords:

• Singular perturbations
• Convection–diffusion
• Interior layer

Keywords:

• 2000 Mathematics Subject Classifications: 35J25
• 35R05

Acknowledgements

Research supported by the Department of Mathematics and the Industrial Mathematics Institute at the University of South Carolina, and by the Boole Centre for Research in Informatics at the National University of Ireland, Cork.