 Outer-edge source of a viscous disk

A narrow surface density of a disk source approaching the outer edge from inside, with $S=S_0\delta (r-r_2)$ normalized to have full weight, gives $\dot{M}=2\pi r_2{S}_0$ and the displayed steady interior profile. This follows by replacing the inner source integral by $r_2{S}_0$ and integrating $u^{-1/2}$. The flux jumps from $\dot{M}$ just inside to zero outside the injecting edge. Thus a zero exterior flux is consistent, whereas a continuous zero interior boundary trace is not. A half-weight convention for a symmetric endpoint Dirac delta function represents a different total injected mass; it must not be silently mixed with the full-weight boundary source.