 Compact self-similar disk with density-linear viscosity

The Keplerian viscous diffusion equation with the displayed kinematic viscosity has two such nontrivial finite-support self-similar solutions: $a=1$, $R=C{t}^{2/5}$, and $a=5/4$, $R=C{t}^{1/2}$. Both have $\sigma =(15At{)}^{-1}$ for $A,C,t>0$. Matching powers of radius eliminates the third power only when $(5/2-2a)(2-2a)=0$. The first solution conserves disk angular momentum; the second conserves disk mass but requires an inner torque.