Drift-Diffusion Past a Circle: Shadow Region Asymptotics
Sean Lynch, Charles Knessl · SIAM Journal on Applied Mathematics · 2009
We consider the steady state concentration of some diffusing substance, subject to a uniform drift field, past a circular obstacle. We obtain some exact representations of the concentration profile of the substance exterior to the obstacle. These representations are particularly useful for studying the solution in ranges of space where the concentration is very small (the “shadow” regions). We assume then that the drift dominates diffusion and obtain various asymptotic expansions in the shadow regions.