Singular perturbation analysis of drift-diffusion past a circle: shadow region
S. Lynch, Charles Knessl · IMA Journal of Applied Mathematics · 2011
We consider steady state drift–diffusion of some substance past a circular obstacle. We obtain asymptotic representations of the concentration profile of the substance exterior to the obstacle. We assume that the drift dominates diffusion and obtains various asymptotic expansions in the ‘shadow’ regions, where the concentration is very small. We apply singular perturbation methods to the governing partial differential equation. Numerical studies are used to back up the asymptotic results.