= Keplerian disk evolution with a ring source
{c}
{title2=$\Sigma_t=\frac3R\partial_R[R^{1/2}\partial_R(\nu\Sigma R^{1/2})]+\frac{\dot M(t)}{2\pi R_0}\delta(R-R_0)$}
For an axisymmetric <thin disc> supplied at $R_0$ with the local <Keplerian rotation> specific angular momentum, the displayed source augments the <Keplerian viscous diffusion equation>. The radial velocity remains $v_R=-3(\Sigma R^{1/2})^{-1}\partial_R(\nu\Sigma R^{1/2})$: subtracting local specific angular momentum times <conservation of mass> from <conservation of angular momentum> cancels the source term. The normalization of the <Dirac delta function> makes the integrated supplied mass per unit time equal to $\dot M(t)$.
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