Heat-equation transform for linear-radius disk viscosity
= Heat-equation transform for linear-radius disk viscosity
{title2=$\bar\nu=\nu_0r,\quad x=2\sqrt{r/(3\nu_0)},\quad g=r^{3/2}\Sigma,\quad g_t=g_{xx}$}
For source-free <Keplerian viscous diffusion equation>, the variables $y=\sqrt r$ and $g=r^{3/2}\Sigma$ give $g_t=(3\nu_0/4)g_{yy}$ when $\bar\nu=\nu_0r$. Rescaling y gives the displayed <heat equation>. Initial and radial boundary conditions must also be transformed; the reduction does not specify them.