= Constant-concentration inlet solution
{title2=$C=\frac12\operatorname{erfc}\frac{x-Ut}{2\sqrt{Dt}}+\frac12e^{Ux/D}\operatorname{erfc}\frac{x+Ut}{2\sqrt{Dt}}$}
= Ogata-Banks solution
{c}
{synonym}
The half-line solution of $C_t+UC_x=DC_{xx}$ with initially zero concentration, unit inlet concentration for positive time, and decay at infinity at fixed time. Both <complementary error functions> are needed to satisfy the inlet exactly. A <Laplace transform> gives $\widetilde C=p^{-1}e^{(U-\sqrt{U^2+4Dp})x/(2D)}$. A finite layer requires an additional downstream boundary condition.
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