= Accreting similarity disk with viscosity proportional to radius
For $\bar\nu=Ar$ with $A>0$, use $x=2\sqrt{r/(3A)}$ and $g=Ar^{3/2}\Sigma$. The <Keplerian viscous diffusion equation> becomes $g_t=g_{xx}$. The <zero-torque inner boundary condition> is $g(0,t)=0$, and the positive solution $g=Cxt^{-3/2}e^{-x^2/(4t)}$ gives $\Sigma\propto r^{-1}t^{-3/2}e^{-r/(3At)}$. Its mass is proportional to $t^{-1/2}$, <angular momentum> is constant and inward mass flow at the origin is proportional to $t^{-3/2}$. Its radial <velocity> is $r/t-3A/2$, exhibiting inner accretion and outer spreading.
// Target: astrophysics.bigb
Back to article page
